MS 1 – Concepts from complex systems – Networks, synchronisation, recurrence

Convener: Sarika Jalan, Maria Carmen Romano
Room: auditorium

Wednesday, March 15th, 16:50–18:20

16:50–17:05 G. Ambika (online) Dynamical transitions on multiplex networks
The real-world complex systems with multiple types of dynamics and multiple types of interactions among them, can be effectively modeled using the framework of multiplex networks. In this talk I will present the emergence of spatio-temporal patterns among dynamical systems connected on a multiplex framework. I will focus mainly on the transfer or selection of activity patterns between collection of neurons and emergence of stable amplitude chimeras and chimera death induced by multiplexing. The occurrence of explosive synchronization and other sudden transitions or tipping induced in a collection of systems due to multiplexing will also be presented.

17:05–17:20 Sarika Jalan Adaptation in higher-order interactions: Explosive transition to cluster synchronisation
So far, all the studies on adaptation in networks have revolved around pair wise interactions. Breaking away from the traditional approach of assuming adaptation in the pairwise coupling, we consider adaptation in higher-order couplings, and show that dynamically adaptive simplicial couplings give birth to cluster (de)synchronization. Notably, the global synchronization which is a prominent feature for non-adaptative simplicial complexes is entirely suppressed as a consequence of adaptation. We develop an analytical framework based on Ott-Antonsen approximation for coupled phase oscillators on adaptive higher order interaction networks, which fully explain the origin of abrupt cluster synchronization and desynchronization.

17:20–17:35 M. Kumar, Mihael Rosenblum High-order phase reduction explains remote synchrony in a chain of Stuart-Landau oscillators
Remote synchronization implies that oscillators interacting not directly but via an additional unit (hub) adjust their frequencies and exhibit frequency locking while the hub remains asynchronous. In this paper, we analyze the mechanisms of remote synchrony in a small network of three coupled Stuart-Landau oscillators using recent results on higher-order phase reduction. We analytically demonstrate the role of two factors promoting remote synchrony. These factors are the nonisochronicity of oscillators and the coupling terms appearing in the second-order phase approximation. We show a good correspondence between our theory and numerical results for small and moderate coupling strengths.

17:35–17:50 Peter beim Graben, Axel Hutt, Serafim Rodrigues Recurrence structure analysis of neurophysiological data
Recurrence is ubiquitous in complex nonlinear systems and can be studied by means of recurrence plots (RP) and recurrence quantification analyses (RQA). Another possibility is to consider the RP as a recurrence grammar which substitutes large time indices from a time series by the smallest, recurrent ones, thereby leading to a coarse-grained representation of the system’s recurrence structure through symbolic dynamics [1,2]. Under two reasonable assumptions about the distribution of the system’s recurrence domains, we suggested two possible utility functions for the optimization of the RP threshold parameter. First, assuming a uniform distribution of recurrence domains and non-recurrent transients over time, we postulated a maximum entropy criterion for the symbolic sequences [1,2]. Second, regarding recurrence domains as metastable states, we derived a utility function for an optimal Markov chain model [3]. In our contribution we compare both approaches by means of numerical simulation results and neurophysiological time series from event-related brain potentials [2,4], resting state fMRI data [5] and animal local field potentials [3].

[1] beim Graben, P. & Hutt, A. (2013). Detecting recurrence domains of dynamical systems by symbolic dynamics. Physical Review Letters 110(15), 154101.

[2] beim Graben, P. & Hutt, A. (2015). Detecting event-related recurrences by symbolic analysis: Applications to human language processing. Philosophical Transactions of the Royal Society London, A373, 20140089.

[3] beim Graben, P., Sellers, K. K., Fröhlich, F. & Hutt, A. (2016). Optimal estimation of recurrence structures from time series. EPL Europhysics Letters, 114, 38003.

[4] Hutt, A. & beim Graben, P. (2017). Sequences by metastable attractors: interweaving dynamical systems and experimental data. Frontiers in Applied Mathematics and Statistics, 3, 11.

[5] beim Graben, P., Jimenez-Marin, A., Diez, I., Cortes, J. M., Desroches, M. & Rodrigues, S. (2019). Metastable resting state brain dynamics. Frontiers in Computational Neuroscience, 13, 62.

17:50–18:00 Steve J. Kongni, Thierry Njougouo, Patrick Louodop, Robert Tchitnga, Hilda A. Cerdeira Phase transition to Synchronization in a System of Swarmalators
Systems of oscillators called Swarmalators, whose phase and spatial dynamics are coupled, have been used to describe the dynamics of some living systems. Their collective behavior presents simultaneous aggregation in space and synchronization in phase which in some cases leads to explosive synchronization in a finite population as a function of the coupling parameter between the phases of the internal dynamics. We describe this phenomenon using the order parameter and the Hamiltonian formalism. Near the synchronization transition the phase energy of the particles are represented by the XY model, and they undergo a transition which can be of the first order or second depending on the distribution of natural frequencies of the internal dynamics of the swarmalators.

18:00–18:10 Timo Bröhl, Klaus Lehnertz A Perturbation-Based Approach to Identifying Superfluous Network Constituents
Constructing networks from empirical time series data is often faced with the as yet unsolved issue of how to avoid superfluous network constituents. Such constituents can result, e.g., from spatial and temporal oversampling of the system's dynamics, and neglecting them can lead to severe misinterpretations of network characteristics ranging from the global to the local scale. We deduce deduce a perturbation-based method to identify superfluous network constituents that makes use of vertex and edge centrality concepts by investigating the influence of removing and cloning single constituents on these global and local network characteristics. We demonstrate the suitability of our approach through analyses of paradigmatic network models with adjustable built-in superfluous constituents.

18:10–18:20 Géza Ódor, Shengfeng Deng, Bálint Hartmann, Jeffrey Kelling Non-local cascade failures and synchronization dynamics on European and US power grids
Dynamical simulation of the cascade failures on the EU and USA high-voltage power grids has been done via solving the second-order Kuramoto equation. We show that synchronization transition happens by increasing the global coupling parameter $K$ with meta-stable states depending on the initial conditions so that hysteresis loops occur. We provide analytic results for the time dependence of frequency spread in the large $K$ approximation and by comparing it with numerics of $d=2,3$ lattices, we find agreement in the case of ordered initial conditions. However, different power-law (PL) tails occur, when the fluctuations are strong. After thermalizing the systems we allow a single line cut failure and follow the subsequent overloads with respect to threshold values $T$. The PDFs $p(N_f)$ of the cascade failures exhibit PL tails near the synchronization transition point $K_c$. Below $K_c$ we find signatures of $T$-dependent PL-s, caused by frustrated synchronization, reminiscent of Griffiths effects [1]. Here we also observe stability growth following blackout cascades, similar to intentional islanding, but for $K > K_c$ this does not happen. For $T < T_c$, bumps appear in the PDFs with large mean values, known as ``dragon king'' blackout events. We also analyze the delaying/stabilizing effects of instantaneous feedback or increased dissipation and show how local synchronization behaves on geographic maps. We demonstrate the occurrence of non-local cascade failure events at the weak points of the networks.

[1] Entropy 22 (2020) 666

[2] Phys. Rev. E 106 (2022) 034311.

Friday, March 17th, 14:00–15:30

14:00–14:15 Georgios Balasis Complex Systems Perspectives Pertaining to the Research of the Geospace Environment
Learning from successful applications of methods originating in statistical mechanics, complex systems science, or information theory in one scientific field (e.g., atmospheric physics or climatology) can provide important insights or conceptual ideas for other areas (e.g., space sciences) or even stimulate new research questions and approaches. For instance, quantification and attribution of dynamical complexity in output time series of nonlinear dynamical systems is a key challenge across scientific disciplines. Especially in the field of space physics, an early and accurate detection of characteristic dissimilarity between normal and abnormal states (e.g., pre-storm activity vs. magnetic storms) has the potential to vastly improve space weather diagnosis and, consequently, the mitigation of space weather hazards. We provide an overview on existing nonlinear dynamical systems-based methodologies along with key results of their previous applications in a space physics context, which particularly illustrates how complementary modern complex systems approaches have recently shaped our understanding of nonlinear magnetospheric variability.

14:15–14:25 Gorka Zamora Lopez, Matthieu Gilson Perturbation-based graph theory: An integrative dynamical perspective for the study of complex networks
Built upon the shoulders of graph theory, the field of complex networks has become a central tool for understanding complex systems. Represented as a graph, empirical systems across domains can thus be studied using the same concepts and the same metrics. However, this simplicity is also a major limitation since graph theory is defined for a binary and symmetric description where the only relevant information is whether a link exists or not between two vertices. The adaptation of graph theory to weighted networks has been rather clumsy with approaches that typically ignore the fact that link weights are not numerical values but represent physical or statistical quantities.
Here, we propose a dynamical reformulation of graph theory that can help aleviate these limitations. First, we show that classical graph metrics are derived from a simple but common generative dynamical model (a discrete cascade) governing how perturbations propagate along the network. This finding exposes that -- contrary to common belief -- graph analysis is a model-based analysis method instead of a data-driven one. From the dynamical perspective graph metrics are no longer regarded as combinatorial attributes of a graph, but correspond to spatio-temporal properties of the network's response to external perturbations.

Second, we learn that many of the limitations of graph theory can be leveraged by replacing the underlying discrete cascade by other generative models which allow for the propagation of continuous variables in continuous time. In practice, our formalism consists in redefining graph metrics from the Green's function of a network. Given an adjacency matrix $A$ we define its Green's function $\mathcal{C}(t)$ for a propagation model of choice. At each time point $t'$, $\mathcal{C}_{ij}(t')$ is a matrix encoding the response of node $j$ to an initial unit perturbation at node $i$. Last, we provide examples of how the perturbation-based analysis helps overcome common issues of graph analysis such as the definition of graph distance in weighted graphs and the comparison of networks of different size or density.

In summary, we propose a dynamical formulation of graph theory in which the underlying generative model is explicit and tunable. This allows to define metrics in which both directionality and link weights are natural -- built-in -- aspects of the metrics. It also provides the oportunity to calibrate network analyses by choosing generative models that are well suited for the particular system under study; thus balancing between simplicity and interpretability of results.

14:25–14:35 Jose M. Amigo, Roberto Dale, Piergiulio Tempesta Complexity-based permutation entropies: From deterministic time series to white noise
Complexity in symbolic times series, symbols being taken from a finite alphabet, has to do with the number of different sequences (strings, words, blocks,\dots) of a given length L and how this number increases with L. The perhaps simplest approach consists in counting the number of such sequences. In this case, the complexity of periodic sequences is a bounded function of L, while the complexity of arbitrary sequences grows exponentially with L. Hence, taking the logarithm is a good idea to distinguish polynomial from exponential growth. Moreover, the limit of the logarithmic growth rate with increasing lengths produces a finite number that is independent of length and, hence, intrinsic to the time series.
Otherwise, if the alphabet is continuous, the situation is more complicated. Such is the case with observations from nonlinear processes and continuous-valued random processes. In this event, one usually divides the alphabet into bins or, as in the ordinal methodology, represents each block by the permutation obtained by ranking the observations in the block. The trouble with the latter option is that the growth of permutations with the length becomes super-exponential in the case of noisy and random signals, which prevents a theoretical definition of "permutation complexity" (say, the permutation entropy rate) along the standard lines sketched above. In this talk we borrow ideas from statistical physics (e.g., group entropy and extensivity) and complexity theory (e.g., complexity classes) to extend the conventional permutation entropy from the exponential class to other complexity classes (polynomial, factorial,\dots) in such a way that the entropy rate of each extension is finite on the corresponding complexity class.

14:35–14:45 P. Haerter, Ricardo Viana Synchronization of phase oscillators due to nonlocal coupling mediated by the diffusion of a substance
Many systems of physical and biological interest are characterized by assemblies of phase oscillators whose interaction is mediated by a diffusing chemical. The coupling effect results from the fact that the local concentration of the mediating chemical affects both its production and absorption by each oscillator. Since the chemical diffuses through the medium in which the oscillators are embedded, the coupling among oscillators is non-local: it considers all the oscillators depending on their relative spatial distances. We considered a mathematical model for this coupling, when the diffusion time is arbitrary with respect to the characteristic oscillator periods, yielding a system of coupled nonlinear integrodifferential equations which can be solved using Green functions for appropriate boundary conditions. In this paper we show numerical solutions of these equations for three finite domains: a linear one-dimensional interval, a rectangular, and a circular region, with absorbing boundary conditions. From the numerical solutions we obtain we investigate phase and frequency synchronization of the oscillators, with respect to changes in the coupling parameters for the three considered geometries.

14:45–14:55 M. Carmen Romano, Ian Stansfield, Pierre Bonnin, Norbert Kern, Alexander Groh, Scott Angus, Tomas Gouveia Patient flow through a hospital: A combined data-driven and modelling approach
One of the biggest challenges faced by hospitals is managing elective care delivery alongside large numbers of emergency admissions, causing rapid growth of elective care waiting times. Mechanisms to improve patient flow through hospitals are urgently needed, but the uncertainty of when patients will be discharged is a major barrier to admissions planning. Hence, the development of a mathematical framework to predict patients’ discharge times and optimise patient flow is crucial to identify bottlenecks and optimisation strategies to alleviate pressures on hospital staff, directly translating into improved healthcare for patients.
In this talk I will present an integrated modelling and data-driven approach to describe patient flow through a hospital and predict hospital length of stay. Based on a publicly available, extensive dataset from intensive care patients in a Boston hospital (MIMIC-III), we show how a neural network approach is able to predict hospital length of stay. Moreover, a mathematical transport model will be presented to describe patient flow through the network of wards in a hospital, taking into account key characteristics governing patient flow, such as ward capacity and state of patients.

14:55–15:05 Oleh Omel'chenko Periodic orbits in the Ott-Antonsen manifold
In their seminal paper [Chaos 18, 037113 (2008)], E. Ott and T. M. Antonsen showed that large groups of phase oscillators driven by a certain type of common force display low dimensional long-term dynamics, which is described by a small number of ordinary differential equations. This fact was later used as a simplifying reduction technique in many studies of synchronization phenomena occurring in networks of coupled oscillators and in neural networks. Most of these studies focused mainly on partially synchronized states corresponding to equilibrium-type dynamics in the so called Ott-Antonsen manifold. Going beyond this paradigm, in this talk, I propose a new approach for the efficient analysis of partially synchronized states with non-equilibrium periodic collective dynamics. The approach is based on the observation that the Poincar{'e} map of the complex Riccati equation, which describes the dynamics in the Ott-Antonsen manifold, coincides with the well-known M{"o}bius transformation. The possibilities of the proposed method are illustrated by its application to the analysis of travelling and breathing chimera states as well as moving spiral wave chimeras.

15:05–15:15 Tamás Kovács Exoplanetary mass constraints based on topology of interacting networks
The continuously increasing number of newly discovered worlds outside of our own solar system requires as precise as possible parameter estimations such as planetary masses, orbital characteristics, bulk density, etc. Comprehensive statistical methods and inverse dynamical analyses have been worked out to obtain system parameters from astronomical observations. Nevertheless, the time domain measurements as scalar time series transformed into complex networks serve a powerful tool to investigate dynamical systems via network topology. Many recent works make significant effort to explore the causality relations and coupling directions between connected dynamical systems.
In this study a new estimation procedure of planetary masses is presented making use of eclipse time variation in multi-planetary systems. Due to the gravitational coupling the motion of planets differs from pure Keplerian ellipse resulting in variable orbital periods. Measuring this tiny effect for nearly co-planar planets one is able to reconstruct the trajectories sharing the same phase space. Transforming then the obtained state vectors of the entangled dynamical systems into network representation, it can be shown that the coupling directions between the interacting sub-networks are related to planetary masses relative to each other.

MS 2 – Analysis and modeling of infrastructure networks

Convener: Nora Molkenthin, Dirk Witthaut
Room: lecture room 1

Wednesday, March 15th, 16:50–18:20

16:50–17:02 Anna Büttner, Anton Plietzsch, Mehrnaz Anvari, Frank Hellmann A Framework for Synthetic Power System Dynamics
As power grids are critical infrastructures their structure and functioning are largely kept confidential by grid operators. Thus there is a need for synthetic power grid models in research. A major use case is to generate large data sets of synthetic grids to investigate the dynamic stability of power grids using machine learning. So far, most machine learning projects had to resort to simple models and often homogeneous parameterization to generate large grid ensembles. I will present a modular framework to generate synthetic power grids that considers the heterogeneity of real power grids but remains simple and tractable. The synthetic grids generated are robust and show good synchronization under all evaluated scenarios, as should be expected for realistic power grids.

17:02–17:14 Benjamin Schäfer, Ulrich Oberhofer Physics-inspired machine learning and stochastic models of power grid dynamics
The operation of power systems is affected by diverse technical, economic and social factors. Social behaviour determines load patterns, electricity markets regulate the generation and weather-dependent renewables introduce power fluctuations. Thus, power system dynamics must be regarded as a non-autonomous system whose parameters vary strongly with time. However, the external driving factors are usually only available on coarse scales and the actual dependencies of the dynamic system parameters are generally unknown. Here, we propose a physics-inspired machine learning model that bridges the gap between large-scale drivers and short-term dynamics of the power system. Integrating stochastic differential equations and artificial neural networks, we construct a probabilistic model of the power grid frequency dynamics in Continental Europe. We complement this machine-learning approach with stochastic models for island power grids, such as Ireland and Iceland. We demonstrate how our models generate synthetic time series, which successfully reproduce central characteristics of the grid frequency. All in all, our work emphasises the importance of modelling power system dynamics as a stochastic non-autonomous system with both intrinsic dynamics and external drivers.

17:14–17:26 Bálint Hartmann How grid information affects the perception of vulnerability of the power grid under physical attacks
Tolerance of the power grid against physical intrusions has gained importance in the light of various attacks that have taken place around the world. To adequately prepare for such events, grid operators have to possess a deep understanding of their infrastructure, more specifically, of its weaknesses. A graph representation of the Hungarian power grid was created in a way that the vertices are generators, transformers, and substations and the edges are high-voltage transmission lines. All transmission and sub-transmission elements were considered, including the 132 kV network as well. The network is subjected to various types of single and double element attacks, objects of which are selected according to different aspects. In all cases, damage is calculated for unweighted and weighted networks as well, to enable the comparison of those two models. Comparison of the damage measured in the unweighted and the weighted network representations shows that damage to the weighted network tends to be bigger for vertex attacks, but the contrary is observed for edge attacks. Numerical differences between the two representations do not show any trend that could be generalised, but in the case of the most vulnerable elements significant differences were found in damage measures, which underlines the importance of using weighted models.

17:26–17:38 Mehrnaz Anvari Hurricane-induced failures of critical transmission lines lead to huge power outages in Texas
Recent reports from various places indicate that electrical infrastructures are hit increasingly by extreme wind events leading to power outages in the system. The Texas electric grid in the Gulf Coast of the United States (US) is a prime example that is frequently hit by hurricanes causing widespread power outages. We here combine a probabilistic line fragility models with a network model of the Texas grid to study the wind-induced failures of transmission lines and the resulting cascading power outages from seven major historical hurricanes. We first identity the most vulnerable sections of the grid. We then show that hardening just a small fraction of critical lines would substantially increase the resilience of the grid to tropical cyclone strikes and could therefore be a viable means to adapt to the projected frequency increase of very intense hurricanes.

17:38–17:50 Narges Chinichian, Gregory Ireland, Pierre-Francois Duc, Clara Neyrand, Philipp Blechinger Estimating electricity demand profile of rural and peri-urban Nigerian households
Reaching SDG7 (Ensure access to affordable, reliable, sustainable, and modern energy for all) in rural and peri-urban underserved communities necessitates a comprehensive understanding of the potential electricity demand of these target communities. In the scope of the PeopleSuN project (People Power: Optimizing off-grid electricity supply systems in Nigeria), 3,599 Nigerian households and 1,122 small and medium-sized enterprises (SMEs) in communities with electricity access outside of urban cores across broad geographic and socioeconomic contexts of Nigeria were surveyed.
The surveys captured household data on socioeconomic and demographic characteristics, expenditures on different household needs, electricity access types and quality, electrical appliance ownership and usage preferences , and usage of different cooking stoves and fuels. More than half of respondents reported a low-quality national grid connection with less than 8 hours of supply per day [1]. We use this data, and its geospatial correlates, to model different archetypical electricity demand profiles at 1-minute resolution for Nigerian households and SMEs using the bottom-up stochastic RAMP model [2]. The model works by simulating the ownership of appliances, their electrical characteristics, and their usage time preferences. The demand profiles resulting from RAMP will then be made publicly available as an open-access dataset for the next steps of the project.

The final product of the project will be an online spatially explicit tool for planning and costing electricity supply solutions [on and off-grid] for non-electrified or weakly electrified areas assuming the archetypical user demands modelled here. This integrated tool is expected to be released in the second half of 2023. We would like to introduce our survey data, demand profiles, and methods to the nonlinear modelling community, receive feedback and form potential further collaborations to develop reliable and open scientific methodologies for planning energy access for underserved communities.

PeopleSuN is a project funded by the German Federal Ministry of Education and Research (BMBF).


[1] Setu Pelz et al. A novel survey dataset for analysing electricity supply and use among rural and peri-urban households and small firms in Nigeria. In:(2022)

[2] Francesco Lombardi et al. Generating high-resolution multi-energy load profiles for remote areas with an open-source stochastic model. In:Energy 177 (2019), pp. 433-444.

17:50–18:02 Naoya Fujiwara Human mobility networks and their applications
Human mobility plays a crucial role in the human activities in cities. It represents not only our daily activities related with locations such as commuting, shopping, and long-distance travels, but also response to abnormal events such as evacuation from disasters and mobility reduction to mitigate spread of infectious diseases. By quantifying the human mobility associated with such activities, we have insights into these issues, which give us clues to better solve such problems. Development of smart phones enables us to acquire big human mobility data with high spatial and time resolution. In particular, time resolution of the mobility data can be less than minutes and duration of the data recording becomes the order of decade. This extends the possible time scales for the analysis including short-time event such as evacuation and long-time event such as migration. A wide variety of tools, which have been proposed recently, enables us to analyze human mobility based on such data much more precisely than before. There are various ways of expressing human mobility. One of the typical ways to express macroscopic flows of people is to count the number of trips between locations, which can be regarded as a network characterized by the origin-destination matrix. Therefore, network analysis is quite important, and various methods have been proposed and applied to analyze the human mobility network. Modelling techniques for reproducing human mobility patterns in various spatial and time scales have been also developed thanks to the enhanced data availability. For example, a model for the travel distance of individuals has been proposed, and some conventional models have been updated.
Here, recent developments of the data analysis, mathematical models and theories of human mobility are reviewed. Possible applications of the analysis of the human mobility networks to social problems such as understanding the change in the mobility under the intervention policies against the spread of an infectious disease are presented.

18:02–18:14 Christoph Steinacker, David-Maximilian Storch, Marc Timme, Malte Schröder Demand-driven design of bicycle infrastructure networks
Sustainable urban transportation critically relies on a sufficiently developed infrastructure. However, designing efficient infrastructure networks constitutes a highly complex problem that requires balancing multiple, often opposing, constraints. Bike path networks in particular need to enable both safe and direct travel for all cyclists with an often strongly limited budget and strong competition for limited road space.
Here, we present a framework to create a sequence of efficient bike path networks by reversing the network formation process and iteratively removing bike paths from an initially complete bike path network. During this process, we continually update cyclists’ route choices, explicitly taking into account the cyclists’ demand and their safety and convenience preferences. In this way, we ensure that the networks are always adapted to the current cycling demand. The framework may thus enable the theoretical study of structural properties of efficient bike path networks across cities and quantify the inherent impact of the demand distributions and street networks on a cities bikeability.

MS 3 – Adaptive and multistable networks

Convener: Serhiy Yanchuk, Tomasz Kapitaniak
Room: lecture room 3

Thursday, March 16th, 9:00–10:30

9:00–9:12 Eckehard Schöll Partial Synchronization Patterns and Chimera States in Adaptive Networks
We review partial synchronization patterns emerging in networks of adaptively coupled nonlinear oscillators. Power grids, as well as neuronal networks with synaptic plasticity, and physiological networks of the immune system and the parenchyma coupled adaptively by cytokines, describe real-world systems of tremendous importance for our daily life. This contribution provides a new perspective by demonstrating that power grids can be viewed as a special class of adaptive networks, where the coupling weights are continuously adapted by feedback of the dynamics, and both the local dynamics and the coupling weights evolve in time as co-evolutionary processes [1]. Such adaptive networks are very common in neural networks with synaptic plasticity. In terms of power grids, the power flow into the network nodes from other nodes represent pseudo coupling weights. This modelling approach allows one to transfer methods and results from neural networks, in particular the emergence of solitary states [2] and multifrequency clusters [3], which may form in a hierarchical way and destabilize the desirable completely synchronized operating state of the power grid. In this work, the relation between these two types of networks, in particular the model of Kuramoto-Sakaguchi phase oscillators with inertia (swing equation for power grids) and the model of phase oscillators with adaptivity, is used to gain insights into the dynamical properties of solitary states and multifrequency clusters in power grid networks. Furthermore, with adaptively coupled phase oscillators in a 2-layer physiological network we present functional modeling of tumor disease and sepsis [4,5].

[1] R.~Berner, S.~Yanchuk, and E.~Sch{\"o}ll: What adaptive neuronal networks
teach us about power grids, Phys. Rev. E 103, 042315 (2021).

[2] H.~Taher, S.~Olmi, and E.~Sch{\"o}ll: Enhancing power grid synchronization
and stability through time delayed feedback control, Phys. Rev. E 100, 062306 (2019).

[3] R.~Berner, S.~Vock, E.~Sch{\"o}ll, and S.~Yanchuk: Desynchronization
transitions in adaptive networks, Phys. Rev. Lett. 126, 028301 (2021).

[4] Sawicki, J., Berner, R., L{\"o}ser, T., and Sch{\"o}ll, E.: Modeling tumor disease and sepsis by networks of adaptively coupled phase oscillators, Frontiers Netw. Physiology 1, 730385 (2022)

[5] Berner, R., Sawicki, J., Thiele, M., L{"o}ser, T., and Sch{\"o}ll, E.: Critical parameters in dynamic network modeling of sepsis, Frontiers Netw. Physiol. 2, 904480 (2022)

9:12–9:24 Celik Ozdes, Deniz Eroglu, Norbert Marwan Tobias Braun Multi-stable synchronization patterns and switching dynamics of paleoclimate networks
To improve our understanding of climate dynamics, we first need to deeply understand the climate’s past if we hope to mitigate and adapt to oncoming critical climate change. Understanding the past climate dynamics depends on the interpretation of paleo proxies. Blending dynamical systems theory, recurrence theorem, multi-stability, and synchronization with complex networks theory and machine learning techniques have become instrumental for a more profound understanding of climate dynamics in the last few decades. However, these techniques are not directly applicable to paleoclimate research since the proxy data is subject to different distortions. The paleoclimate proxy measurements carry uncertainty in nominal and temporal dimensions, and also the choice of proxy and varying effects of local and global interactions matter.
Paleoclimate proxies typically represent the climate dynamics of large spatial regions and long periods. Furthermore, the proxies contain many switching transitions between droughts and wet seasons, showing that paleoclimate dynamics have multi-stability. To mimic paleoclimate dynamics, we introduce a multi-layer network model of coupled chaotic maps where multiple chimera configurations of synchronized subsystems co-exist as stable states. This multi-stable system goes through a series of critical transitions into another stable state through noise induction. We collect only the mean field of the state variables from each layer to imitate the spatial sparsity of paleoclimate measurements. Using this limited information, we developed a methodology to reconstruct paleoclimate networks and identify the critical switching of dynamical patterns.

Our paleoclimate network approach pivots around the recurrent property of climate system states. After suitable transformations, recurrence quantification analyses (RQA) of proxy series are shown to be robust indicators of the dynamical properties of represented dynamics in the form of time series. We construct a functional network from these series with nodes representing proxy sources using the time evolution of individual series. This allows us to classify the system state with respect to the visible relational dynamics between nodes. We also extended our studies to real paleoclimate datasets around Northern Africa and found the dominant dynamical patterns associated with known periods.

9:24–9:36 Christian Bick, Tobias Böhle, Christian Kühn Bifurcations of Twisted States in Phase Oscillator Networks
The Kuramoto model provides a prototypical framework to study the dynamics of interacting particle systems. The classical heterogeneous Kuramoto model exhibits two main dynamically important states - desynchronization and partial synchronization. Depending on the parameters of the system, the long term behavior always tends to either of these states. However, when considering identical oscillators on a nearest-neighbor graph, the Kuramoto model exhibits more interesting states such as uniformly twisted states. It was discovered by Wiley, Strogatz and Girvan in 2006 that the stability of these twisted stated depends on the coupling range of the nearest-neighbor graph. Since this original analysis was published, many generalizations and variants were developed. In this talk, we will analyze the bifurcation in which these twisted states lose their stability upon varying parameters, such as the coupling range, of the system. We investigate the existence and shape of bifurcating equilibria in the infinite particle limit.

9:36–9:48 Luis Guillermo Venegas Pineda, Hildeberto Jardón-Kojakhmetov, Ming Cao Generating stable chimera states in adaptive networks
During the past decades, chimera states have attracted substantial attention due to their unexpected symmetry broken spatio-temporal nature, enabling the coexistence of synchronous and incoherent behaviours in complex networks under particular conditions. Despite relevant results of such unforeseen states in different physical and topological configurations have been obtained, there remain several structures and mechanisms yet to be unveiled. In this talk, I will present a novel technique for the generation of different synchronization patterns, including stable chimera states, by introducing adaptation in the coupling strengths. For this matter, we study a multilayer network composed by two populations of heterogeneous Kuramoto phase oscillators with coevolutive couplings only dependent on macroscopic quantities of the system. Moreover, due to the nature of the model and by taking the continuum limit, we derive a mean-field representation for which we employ geometric singular perturbation theory (GSPT) by including a time-scale separation between the dynamics of the nodes and their connections. Subsequently, I address two different problems, namely the coevolutive inter and intracoupling scenarios, for which I present necessary and sufficient conditions for the critical manifold to be normally hyperbolic and attracting in the entire domain of interest. Moreover, I will emphasize the effect of the selected slow adaptation rule in the formation of different synchronization patterns in the mean-field. On top of that, considering the previous conditions and the stability of the coupling dynamics, I give arguments for the preservation of such behaviors at the network level, supported by numeric results for several synchronization arrangements. Lastly, I present simulations of the non-hyperbolic case for which relaxation oscillations and canard cycles, related for the first time to breathing chimera states, have been observed.

9:48–10:00 Rico Berner Adaptivity and multi-mode-induced multistability in coupled oscillator systems
Multistability, the co-emergence of collective states and synchronization patterns, plays an important role in mathematics and physics, e.g., for the modeling of climate systems or the understanding of the dynamic coordination in the brain. Different mechanisms inducing multistability in complex dynamical systems have been described. In this talk, we show how an adaptive network structure or the interplay of multiple modes in the interaction function provide the necessary flexibility for the co-stability of different dynamical states in systems of coupled phase oscillators. We identify the systems' main features leading to multistability and discuss the implications of multistability for their complex phase transitions. In particular, we present a transition phenomenon in an adaptive dynamical network that is similar to heterogeneous nucleation induced by local impurities known, e.g., from cloud formation, crystal growth or Ostwald ripening in equilibrium and nonequilibrium systems.

10:00–10:12 Tomasz Burzynski, Przemyslaw Perlikowski, Piotr Brzeski Multistable dynamics of church bell system
We present how sample-based analysis can complement classical methods for the analysis of dynamical systems. We use it to detect the multistability in the non-linear, piecewise, and discontinuous system. We base on the yoke-bell-clapper system with variable geometry and adjustable excitation force. A mathematical model base on the existing device. The analysed model can reliably predict the ringing scheme of a bell and associated reaction forces in the supports. We found a wide variety of periodic and non-periodic solutions and examined the ranges of coexistence of solutions and transitions between them via different types of bifurcations.

10:12–10:24 A. A. Nanha Djanan, B. R. Nana Nbendjo Response of Mechanical Structures Supporting DC Motors with Limited Power Supply
The present communication aims to describe the dynamics of mechanical structures such as beam and rectangular plate when they are subjected to one or more DC motors with limited power supply. For that, two main approaches have been developed with the purpose to give a good insight on vibration control and stability of the studied system. The method is rather based on the synchronization with and without delay between the external sources (DC motors) working on the structure. The phase, anti-phase or rapid and late synchronization phenomena between the motors show a big influence on the dynamics response of the system.

10:24–10:30 Tiago Pereira, Carlos Fiore, Ralf Toenjes Coherence resonance in networks
Complex networks are abundant in nature and many share an important structural property: they contain a few nodes that are abnormally highly connected (hubs). Some of these hubs are called influencers because they couple strongly to the network and play fundamental dynamical and structural roles. Strikingly, despite the abundance of networks with influencers, little is known about their response to stochastic forcing. Here, for oscillatory dynamics on influencer networks, we show that subjecting influencers to an optimal intensity of noise can result in enhanced network synchronization. This new network dynamical effect, which we call coherence resonance in influencer networks, emerges from a synergy between network structure and stochasticity and is highly nonlinear, vanishing when the noise is too weak or too strong. This is a joint work with C. Fiore and Ralf Toenjes.

MS 4 – World-earth system analysis

Convener: Jonathan Donges, Jobst Heitzig
Room: auditorium

Thursday, March 16th, 9:00–10:30

9:00– 9:05 Jonathan Donges, Jobst Heitzig Introduction
9:05– 9:25 Wolfram Barfuss Reshaping human-environment modeling
Collective action is crucial to embark on sustainable development pathways. Rapid and large-scale transformation is needed to avoid catastrophic tipping points in increasingly interconnected human-environment systems. However, the question of how collective, cooperative behavior - in which intelligent actors seek ways to jointly improve their welfare in dynamic environments -is unresolved. To make progress in this area, mathematical models are essential. To date, however, no modeling framework can address the elements of collective behavior from intelligent actors in complex biophysical environments in a consistent and understandable manner. In this talk, I'll present an overview of ideas and recent works on moving forward with this challenge and reshaping human-environment modeling.

9:25– 9:40 Alexander Makarenko Toward strict investigation of sustainable development of society: Formalization and models
Concepts and models for sustainable development and transformation of large socials systems are considered. Some ways for formalization of scenarios of transformations are proposed. It is proposed the description of a new approach to mentality accounting in operational research (OR), which is based on internal representation of mental images. There are considered: 1) Sustainable development as a mathematical problem, including a formal definition of sustainable development with ethic accounting. 2) New models of large social systems, 3) The influence of the ethical aspects of the transformation of social systems. 4) Risk assessment in scenarios for large socio- economic systems. 5) Transformation of society. 6) Anticipatory aspects of sustainable development.
In the case of crisis conditions (for example, in a war situation), the variables change very quickly. Therefore, it is necessary to make a special adaptation of the problem of sustainable development to such conditions. Here we note several areas of setting such problems for crisis conditions. They may look differently depending on the scale and aspects under consideration.


1. Makarenko, A.: Sustainable development and principles of social systems modeling. Generis Publisher, 2020. 173 p.

2. Makarenkoo, A.: Collective Properties of Large Social Systems. New Approaches. Taras Shevchenko 6th Int. Conf. on Social Sciences. Kyiv 04-05 April 2021. Vol. 3, p.~911--916. ISBN 978-605-70554-1-5

9:40– 9:55 Nico Wunderling, Saverio Perri, Wolfram Barfuss, Amilcare Porporato, Michael Oppenheimer, Jonathan F. Donges Simon A. Levin, Johan Rockström Concerted efforts of politics, society and science can effectively turn down tipping risks
Several climate tipping elements such as the Amazon rainforest or the large ice sheets on Greenland and Antarctica are showing increasing signs of dramatic change in response to human-made global warming. While dangerous tipping risks can be reduced by keeping strict temperature guardrails set by international agreements, so far, such agreements have prompted only moderate emission cuts due to socio-political challenges. Here, we couple a conceptual model of interacting climate tipping elements to a simplified social model outlining an energy-production transition toward clean energy. Using this coupled model, we find that three ingredients are required for a fast sustainability transition, avoiding the largest tipping risks: (i) Strong political incentives to invest in clean energies, (ii) high societal pressure to avoid crossing climate tipping thresholds, and (iii) scientific guidance leading to sufficiently small uncertainties in tipping points. If these conditions are met, we reveal that tipping risks can be reduced by a factor of up to 20, in particular when uncertainties in tipping element thresholds are reduced significantly.

9:55–10:10 Miguel D. Mahecha, Chaonan Ji, Guido Kraemer, Francesco Martinuzzi, David Montero, Karin Mora, Martin Reinhardt, Maximilian Söchting Uncovering complex dynamics in the Earth system using Earth system data cubes
Analysing Earth system dynamics based on high-dimensional data streams remains a major scientific challenge. However, we need to understand the coupled dynamics of land-atmosphere interactions in order to manage the ecosystems of the future taking into account changes due to increasing intensities of climate extremes, ongoing land cover change, and legacies of past anomalies. In this contribution, we will first present advances in the Earth System Data Cube concept for analysing high-dimensional dynamics in the Earth system. Advances range from interactive visualisations that make terabytes of data accessible to everyone to the latest deep learning applications. Second, we will highlight some scientific advances in understanding the coupled land-atmosphere system in response to climate extremes. Finally, we give an outlook towards considering “biodiversity” as a control of land-surface dynamics.

10:10–10:25 Bernd Blasius Theoretical ecology meets marine geochemistry: Approaching the enigmatic persistence of dissolved organic matter in the oceans
Marine dissolved organic matter (DOM) is a highly diverse mixture of compounds, accounting for one of the Earth’s largest active carbon pools with a similar amount of reduced carbon as all living biomass on land and in the oceans combined. Aquatic organisms continuously release a myriad of organic molecules that become food for microbes, but a residual fraction of DOM resists microbial degradation and accumulates in the ocean for millennia, resulting in the huge standing stock of refractory DOM. The reasons behind this DOM persistence, where starving microbes fail to utilize the energy source of their surrounding organic matter, remain unknown. Here, I present a recently developed model framework that captures the interaction between a complex mixture of DOM compounds and a diverse community of microbial consumers as bipartite networks of DOM release and microbial turnover. Extending classic consumer-resource systems, the model yields surprising rich dynamic structure, including parameter regimes with chaotic dynamics, suggesting that microbial communities in the deep sea are characterized by self-organized temporal fluctuations. Including evolutionary processes, the model predicts a strong diversification of externally supplied DOM that creates niches for invasion of new microbial consumers, yielding cascades of subsequent extinctions of others. This leads to complex co-evolutionary dynamics subject to persisting turnover, even in stable environments. Thereby, microbial communities self-organize into different modules, akin to trophic layers in food-webs, and the system evolves to a state of highly diluted and diverse DOM in which micro-heterotrophs are living at the edge of their fitness range. These model results provide a mechanistic understanding of how the huge recalcitrance and diversity of DOM might emerge from the complex interactions between microbial communities and organic molecules. Finally, I show how implementing the DOM-microbe interactions into a global ocean model allows to capture large-scale DOM patterns in the ocean and to model expected changes of the DOM inventory in future climate scenarios.

10:25–10:30 Jonathan Donges, Jobst Heitzig Wrap-up

MS 5 – Cardiovascular dynamics and sleep disorders

Convener: Niels Wessel, Ulrich Parlitz
Room: lecture room 1

Thursday, March 16th, 9:00–10:30

9:00– 9:15 Thomas Penzel Sleep research using non‐linear analysis supports the understanding of physiological brain functions
Human sleep has been studied using behavioral observation first. Sleep is a state of unconsciousness. Based on behavior and on recording of brain activity, it is possible to distinguish wakefulness, rapid-eye-movement sleep (REM sleep), and non-REM sleep. Non-REM sleep can be further differentiated in light sleep and deep sleep according to the difficulty to wake up a person.
Because sleep is a function not only of the brain, but of the entire body, sleep recording includes the recording of respiration, cardiovascular functions, limb movements, audio and visual channels. All these signals, their recording and their evaluation are specified and described in an international manual for recording and analysis of sleep. These additional signals are of major importance when diagnosing sleep disorders.

Today much is known about the recording of sleep and many efforts take place to automate the analysis of sleep. This analysis has targeted not only the brain signals, but also the other signals and success differs according to the different sources of physiological signals. Taking all signals and analysis results together helps to improve the understanding of normal and disturbed sleep. Linear analysis had long been used for the analysis of these signals. Today non-linear analysis of signals helps to extract characteristic features for the description of sleep and sleep disorders. Now, not only feature extraction, but signals themselves are used for a new analysis of sleep stages and sleep disorders. With increasing computational power new methods for big data analysis can be used to obtain better understanding of physiological functions during sleep.

9:15– 9:30 Dagmar Krefting Measuring synchronization of physiological systems in sleep – Chances and challenges
Synchronization between different physiological systems is examined to investigate their interaction depending on the physiological state, including various disorders. For example, cardio-respiratory synchronization is frequently assessed; and heart and brain interaction is increasingly acknowledged as an important research topic. Synchronization is typically determined by methods of (linear and nonlinear) time-series analysis applied to multidimensional biosignals. However, the complex dynamics of the human physiology as well as the heterogeneity of biosignal measurements and time-scales pose challenges to the applicability of methods of nonlinear data analysis. Robustness and reproducibility of synchronization effects are therefore critical for the interpretation of analysis results. In sleep, different synchronization pattern - that can also be interpreted as different topologies of the human physiological network - have been observed, with deviations in different sleep disorders. Results from these studies are presented and discussed.

9:30– 9:45 Beata Graff, Grzegorz Graff, Krzysztof Narkiewicz Assessment of cardiorespiratory variability from a clinician's perspective
9:45–10:00 Dirk Cysarz, Friedrich Edelhäuser Asymmetries of heart period dynamics assessed by its cumulative accelerations and decelerations
Heart period dynamics can be analyzed by methods derived from symbolic dynamics. A binary series representing the succession of acceleration and deceleration of heart periods still contains relevant information. However, assessing asymmetries in the heart period series needs more information. Here, we aim to complement measures of binary symbolic dynamics by properties closely related to the binary representation, i.e., cumulative accelerations and decelerations of heart period as basic characteristics underlying heart rate variability. The distributions of the accelerations and decelerations were quantified by the shape parameter of the Weibull function. This approach was applied to 1087 RR tachograms from healthy subjects covering the entire adulthood (age range: 18 to 84 years). Each parameter was analyzed per age decade. The average RR interval increased at old age compared to the youngest age group (median RR interval 839 ms vs.~970 ms). SDNN was constant up to 39 years and declined for older subjects (56 ms vs. 36 ms). The median acceleration was not different from the median deceleration in any age group. The shape parameter of the Weibull function differed for accelerations and decelerations in three age groups (20--29, 30--39 and 40--49 years). The median cumulative acceleration was different from the median cumulative deceleration for the age groups 20--29 and 50--59 years. The shape parameters for cumulative accelerations and decelerations were different in all age groups except in older subjects (age groups 70 - 79 and >80 year). The analysis of cumulative accelerations and decelerations complement information derived from the analysis of binary symbolic dynamics. The results provide clear evidence for asymmetries in heart period dynamics.

10:00–10:15 Thomas Lilienkamp, Ulrich Parlitz, Stefan Luther Adapting pulse sequences for an efficient termination of spiral wave chaos
Life threatening cardiac arrhythmia such as ventricular fibrillation are governed by a chaotic electrical excitation wave dynamics, governed by spiral or scroll waves. Several new defibrillation concepts aiming at terminating arrhythmia with reduced side effects in comparison to the conventional method, by using pulse sequences of lower energy. In most of these studies, the temporal distance between consecutive pulses is kept constant. We demonstrate in a numerical study, how adapting the temporal distances between pulses may significantly alter the success rate of pulse sequences.

10:15–10:30 Flavio H. Fenton, Uzelac Ilija, Neal Bhatia, Shahriar Iravanian, Elizabeth M. Cherry Nonlinear dynamics in live explanted human hearts – From spiral waves to unstable periodic orbits including period three and chaos
In this talk we will present experimental data from simultaneous voltage and calcium optical mapping obtained from seven live explanted human hearts (from patients receiving a new heart). We present the first quantitative detailed dynamics of stable functional voltage and calcium spiral waves in the ventricles with both chirality. We also show several examples of period doubling bifurcations, and complex long periodic orbits obtained during fast pacing, including several examples of period three and chaos quantified with a Lyapunov exponent. We then demonstrate how period doubling in space can lead to a complex substrate for the propagation of electrical waves in the human heart that initiate continuous multiple short lived spiral waves resulting in complex spatiotemporal dynamics (fibrillation). Finally, we present a theory of spiral wave “teleportation” that can be used to terminate these multiple spiral waves within one perturbative shock.

MS 6 – Dynamics of complex biological systems

Convener: Alexey Zaikin, Aneta Koseska
Room: auditorium

Friday, March 17th, 11:00–12:30

11:00–11:15 Alexander Auhlela Arnold tongues in mouse embryonic development
We study the origin and function of collective signaling oscillations in embryonic development. Oscillatory signaling is linked to the sequential segmentation of the vertebrate embryo body axis and the formation of pre-vertebrae, somites. Most strikingly, signaling oscillations are coordinated between neighboring cells and result in spatio-temporal wave patterns that traverse the embryo periodically. I will discuss how we employ general synchronisation principles and entrainment to reveal the fundamental dynamical properties of this embryonic coupled oscillator network.

11:15–11:30 Benjamin Lindner Fluctuation-dissipation relations for spiking neurons
Spontaneous fluctuations and stimulus response are essential features of neural functioning but how they are connected is poorly understood. I derive fluctuation-dissipation relations (FDR) between the spontaneous spike and voltage correlations and the firing rate susceptibility for i) the leaky integrate-and-fire (IF) model with white noise; ii) an IF model with arbitrary voltage dependence, an adaptation current, and correlated noise. The FDRs can be used to derive thus far unknown statistics analytically [model (i)] or the otherwise inaccessible intrinsic noise statistics [model (ii)].

11:30–11:42 Mogens Jensen Oscillations, Arnold Tongues and Chaos in Cell Dynamics
When some human cells are damaged or stressed they respond by oscillating protein densities as have been observed for two famous transcription factors p53 and NF-kB (1). The oscillations have a period of 3--5 hours and appear in both healthy and sick cells. p53 is a cancer gene while NF-kB plays a role in diabetes. For p53 we show that that droplets of repair proteins form around damage sites in an oscillating fashion thus preventing Oswald ripening. The period of oscillations provides an optimal time scale for the repair mechanism (2). By apply an external periodic protein signal, the internal oscillation can lock to the external signal and thus controls the genes. The locking occurs when the ratio between the two frequencies is a rational number leading to Arnold tongues. If tongues overlap, chaotic dynamics appear which strongly influence gene production. The oscillations can be used as a diagnostic tool to distinguish different cancers. Our findings are in good agreement with experimental data from our collaborative groups at Harvard Medical, Beijing and Taiwan.

[1] M.L. Heltberg, S. Krishna, L.P. Kadanoff and M.H. Jensen, A tale of two rhythms: Locked clocks and chaos in biology (Review), Cell Systems, 12, 291-303 (2021).

[2] M.S. Heltberg, A. Lucchetti1, F.-S. Hsieh, D.P.M. Nguyen, S.-h.Chen and Mogens H. Jensen, Enhanced DNA repair through droplet formation and p53 oscillations, Cell 185, 4394-4408 (2022).

11:42–11:54 Arkady Pikovsky, Lev Tsimring Statistical Theory of Asymmetric Damage Segregation in Clonal Cell Populations
Asymmetric damage segregation (ADS) is ubiquitous among unicellular organisms: After a mother cell divides, its two daughter cells receive sometimes slightly, sometimes strongly different fractions of damaged proteins accumulated in the mother cell. Previous studies demonstrated that ADS provides a selective advantage over symmetrically dividing cells by rejuvenating and perpetuating the population as a whole. In this work we focus on the statistical properties of damage in individual lineages and the overall damage distributions in growing populations for a variety of ADS models with different rules governing damage accumulation, segregation, and the lifetime dependence on damage. We show that for a large class of deterministic ADS rules the trajectories of damage along the lineages are chaotic, and the distributions of damage in cells born at a given time asymptotically becomes fractal. By exploiting the analogy of linear ADS models with the Iterated Function Systems known in chaos theory, we derive the Frobenius-Perron equation for the stationary damage density distribution and analytically compute the damage distribution moments and fractal dimensions.

11:54–12:06 Bhumika Thakur, Hildegard Meyer-Ortmanns Heteroclinic dynamics as framework for cognitive processes
Heteroclinic dynamics is a suitable framework for describing transient but reproducible dynamics such as cognitive processes in the brain. It allows an implementation of winnerless competition so that different hierarchical processes in time possibly proceed in parallel at different places in space. We demonstrate how heteroclinic dynamical units, assigned to the sites of a grid, can act as pacemakers to entrain larger sets of units from a resting state to hierarchical heteroclinic motion, manifest as fast oscillations modulated by slow oscillations. The entrainment range depends on the type of coupling, the spatial location of the pacemaker and the individual bifurcation parameters of both the pacemaker and the driven units. We demonstrate why noise can considerably facilitate synchronization. Depending on the selected path in the heteroclinic network, units can be synchronously entrained to different temporal patterns. Such patterns are believed to code information in brain dynamics. Depending on the number and the location of pacemakers on a two-dimensional grid, synchronization can be maintained in the presence of a large number of resting state units and mediated via target waves when the pacemakers are concentrated to a small area of such a grid. Under a quench in the bifurcation parameter, hierarchical heteroclinic motion appears to be rather inert. In view of brain dynamics, our results indicate a possibly ample repertoire for coding information in temporal patterns. While these temporal patterns are produced by sets of synchronized units entrained by pacemakers and propagated in space, no finetuning of the parameters is needed for the entrained units.

12:06–12:18 Klaus Lehnertz Network-based approaches to prediction and control of epileptic seizures
Epilepsy is nowadays conceptualized as a large-scale brain network disease with functionally and/or structurally aberrant connections It is one of the most common serious neurological disorders, affecting approximately 65 million people worldwide. Epileptic seizures are the cardinal symptom of this multi-facetted disease and are usually characterized by an overly synchronized firing of neurons. Seizures cannot be controlled by any available therapy in about 25% of individuals. Over the last decades, an improved characterization of the spatial-temporal dynamics of the epileptic process could be achieved with concepts and methods from nonlinear dynamics, statistical physics, synchronization and network theory. I will provide an overview of the progress that has been made using network-based approaches to prediction and control of epileptic seizures and will discuss necessary extensions to further advance the field.

12:18–12:30 Axel Hutt, Jérémie Lefebvre Additive noise-induced stability tuning in neuronal systems
For a long time, multiplicative noise has been known to control the stability and evolution of nonlinear systems, whereas additive noise does not. Today additive noise-induced stability modifications attract more and more attention in theoretical research, e.g., work on stochastic bifurcations [1], random dynamical systems [2] or on stochastic random networks [3]. The presented work illustrates additive noise-induced effects in spatially extended systems [4] and stochastic random networks demonstrating coherence resonance [5]. Models of frequency induction and switching [6] in the brain demonstrate the mechanisms' possible importance in understanding neural processes.
[1] N. Sri Namachchiava, Stochastic Bifurcations, Appl. Math. Comput. 38(2):101-159 (1990)
[2] L. Arnold, Random Dynamical Systems, Springer (1998)
[3] A. Hutt, Front. Appl. Math. Stat. 8:879866 (2022)
[4] A.Hutt et al., Phys. Rev. Lett. 98:230601 (2007)
[5] A. Hutt et al., Front. Appl. Math. Stat. 7:697904 (2021)
[6] A. Hutt et al., NeuroImage 179:414-428 (2018) ; A. Hutt and J. Lefebvre, Brain Top. 35:108-120 (2021)

MS 7 – Nonlinear dynamics in economics

Convener: Giuseppe Orlando, Willi Semmler
Room: lecture room 1

Friday, March 17th, 11:00–12:30

11:00-11:15 Stefan Mittnik Modeling state-dependent dynamics
In many empirical modeling efforts, we encounter phenomena that exhibit state-dependent behavior. The way a dynamic system responds to external influences can vary depending on the state the system is operating in. A wide range of examples can be found in natural and social sciences as well as engineering. Business cycle are a typical example in macroeconomic modeling. External shocks to an economy tend to have very different effects on variables such as employment, growth or inflation, depending on whether the economy is in a period of strong growth or in a recession. So-called state- or regime-dependent modeling strategies have been proposed to model such phenomena. In this contribution, we provide an overview of alternative approaches to state-dependent modeling of dynamic processes and discuss their relevance to specific types of applications.

11:15-11:30 Pu Chen, Willi Semmler (online) Stability in Threshold VAR Models
This paper investigates the stability of threshold autoregressive models. We review recent research on stability issues from both a theoretical and empirical standpoint. We provide a sufficient condition for the stationarity and ergodicity of threshold autoregressive models by applying the concept of joint spectral radius to the switching system. The joint spectral radius criterion offers the most generally applicable criterion to determine the stability in a threshold autoregressive model.

11:30-11:45 Marek Lampart, Alžběta Lampartová, Giuseppe Orlando On risk and market sentiments driving financial share price dynamics
The goal is to investigate the dynamics of banks' share prices and related financials that lead to potential disruptions to credit and the economy. We adopt a classic macroeconomic equilibrium model with households, banks, and non-financial companies and explain both market valuations and endogenous debt constraints in terms of risk. Heterogeneous market dynamics ranging from equilibrium to cycles and chaos are illustrated. Deposits and equity are proven to be management levers for chaos control/anticontrol and the only feasible equilibrium is unstable. Finally, using real-world data, a test is conducted on the suggested model proving that our framework conforms well to reality.

11:45-12:00 Marek Lampart, Alžběta Lampartová, Giuseppe Orlando On extensive dynamics of a Cournot heterogeneous model with optimal response
The aim of this talk is to study the dynamical properties analysis of an original specification of the classical Cournot heterogeneous model with optimal response. The analysis is performed by means of bifurcation diagrams, the 0-1 test for chaos, Power Spectral Density, histograms, and trajectory analysis. For this purpose, a new perturbation parameter of the initial condition is introduced, and together with the intensity of choice parameter, the system is researched. Extreme reach dynamics, coexisting attractors, and periodic and chaotic trajectories are investigated through massive simulations.
This talk is based on the paper: On extensive dynamics of a Cournot heterogeneous model with optimal response, Chaos 32(2) (2022).

12:00-12:15 Jian Kang, Changli He, Annastiina Silvennoinen, Timo Teräsvirta Long Monthly European Temperature Series and the North Atlantic Oscillation
In this presentation, the relationship between the surface air temperatures in 28 European cities and towns and the North Atlantic Oscillation (NAO) is modelled using the Vector Seasonal Shifting Mean and Covariance Autoregressive model, extended to contain exogenous variables. Central statistical and time series features of the model are discussed before moving on to discussing data and showing empirical results. The model also incorporates season-specific spatial correlations that are functions of latitudinal, longitudinal, and elevation differences of the various locations.
The empirical results, based on long monthly time series, agree with previous ones in the literature in that the NAO is found to have its strongest effect on temperatures during winter months. The transition from the boreal winter to the summer is not monotonic, however. The strength of the error correlations of the model between locations is inversely related to the distance between the locations, with a slower decay in the east-west than north-south direction. Altitude differences also matter but only during the boreal winter half of the year.

12:15-12:30 Oliver Richters Modeling the out-of-equilibrium dynamics of bounded rationality and economic constraints
The analogies between economics and classical mechanics can be extended from constrained optimization to constrained dynamics by formalizing economic (constraint) forces and economic power in analogy to physical (constraint) forces in Lagrangian mechanics. In the differential-algebraic equation framework of General Constrained Dynamics (GCD), households, firms, banks, and the government employ forces to change economic variables according to their desire and their power to assert their interest. These ex-ante forces are completed by constraint forces from unanticipated system constraints to yield the ex-post dynamics. The flexible out-of-equilibrium model can combine Keynesian concepts such as the balance sheet approach and slow adaptation of prices and quantities with bounded rationality (gradient climbing) and interacting agents discussed in behavioral economics and agent-based models. The framework integrates some elements of different schools of thought and overcomes some restrictions inherent to optimization approaches, such as the assumption of markets operating in or close to equilibrium. Depending on the parameter choice for power relations and adaptation speeds, the model nevertheless can converge to a neoclassical equilibrium, and reacts to an austerity shock in a neoclassical or post-Keynesian way.

MS 8 – Causation and prediction of weather and climate extremes

Convener: Bruno Merz, Jakob Runge
Room: lecture room 3

Friday, March 17th, 11:00–12:30

11:00–11:05 Jakob Runge, Bruno Merz Introduction
11:05–11:25 Leonard A. Smith (Keynote) A Dynamical Systems View of the Prediction of Extreme Weather Events in a Changing Climate: Insight, Foresight and Attribution
Quantitative insights into likely weather extremes in our future climate are in high demand. Pointed questions from both governments and various industrial sectors for clarification of the current limits to predictability and for interpretation of model output are presented in the context of simulating nonlinear dynamical systems. The probabilistic predictability of a dynamical system is not limited by chaotic dynamics inasmuch as uncertainty in the current state of the state of the system can be propagated into the future; as long as the model is perfect. Prediction via simulation with imperfect models, and the predictability of open systems in general, introduce new challenges both to the scientific community and to the communication of uncertainty and insight. Both types of challenge are illustrated through the analysis of actual probabilistic predictions of weather and of climate.
Interesting dynamical systems questions abound: Is it more useful to maintain a plethora of closely related but distinct mathematical structures of limited complicatedness or focus on a single model structure developed with significantly greater resources (“one model to rule them all”)? Would there be an advantage to constructing somewhat independent models which share today’s best physics and observations, but never see each other’s outputs? Mathematically, what is the most effective way to present the diversity of simulations generated for the advancement of science, or in the support of decision making? In practice, how harmful is opacity (the failure to communicate known limits of today’s simulations clearly) both within the sciences and to decision makers? Should we attempt probabilistic attribution of event with probability of one (as it has already happened) or search to make climate science more predictive for this type of event, by moving to shorter lead times, or by filling a basket of unprecedented events now thought vastly more likely under current conditions (and then noting they had been identified a priori) or by other means?

These questions will be examined from a dynamical systems point of view, enlightened by a good deal of experience with numerate decision makers. A Just Enough Decisive Information (JEDI) approach to applied simulation modelling of weather events in an evolving climate is suggested. The value of accepting that both the expectations from and the analysis of nonlinear models in a weather-like context differs fundamentally from those in a climate-like context is stressed.

11:25–11:40 Elena Surovyatkina Forecasting tropical monsoon: Advances and opportunities
Close to half of the global population relies on the monsoon to collect drinking water, grow crops, and produce electricity. The abruptness of the beginning and end of the rainy season and a month's interannual variability are key features of the phenomenon, thus making monsoon forecasts extremely challenging. The limitations of current models prevent further progress. A new strategy is urgently needed in weather and climate sciences.
Here I show that a new understanding of essential physical mechanisms of monsoon arrival and withdrawal allows more than a month in advance to predict monsoon timing. The approach is fundamentally different from the numerical weather and climate models; it is based on system analysis, statistical physics principles and newly discovered spatial-temporal regularities (or teleconnections between Tipping Elements) in a monsoon system. The forecasting relies on the re-analysis dataset: temperature, relative humidity, and outgoing longwave radiation. The approach implementation is backed up with solid evidence: 7-years-test shows a successful result forecasting 40 days in advance for the onset date and 70 days before the withdrawal date. Applicability of the methodology is not limited by specific location; it works for different parts of India - Central India, Telangana, Delhi, as well in Africa and South America.

11:40–11:55 Milan Paluš Causality in complex systems: Multiple scales and extreme events
Quantification of causality in terms of improved predictability was proposed by the father of cybernetics N. Wiener [1] and formulated for time series by C.~W.J. Granger [2]. The Granger causality evaluates predictability in bivariate autoregressive models. This concept has been generalized for nonlinear systems using methods rooted in Shannon information theory [3,4,5]. This approach, however, usually ignores two important properties of complex systems, such as the Earth climate: the systems evolve on multiple time scales and their variables have heavy-tailed probability distributions. While the multiscale character of complex dynamics, such as air temperature variability, can be studied within the Shannonian framework [6,7], the entropy concepts of Renyi and Tsallis have been proposed for variables with heavy-tailed probability distributions. We will discuss how to cope with multiple scales and how non-Shannonian entropy concepts can be applied in inference of causality in systems with heavy-tailed probability distributions and extreme events. Using examples from the climate system, we will focus on causal effects of the North Atlantic Oscillation, blocking events and the Siberian high on winter and spring cold waves in Europe, including the April 2021 frosts endangering French vineyards.
This study was supported by the Czech Academy of Sciences, Praemium Academiae awarded to M. Palu\v{s}.


[1] N. Wiener, in: E. F. Beckenbach (Editor), Modern Mathematics for Engineers (McGraw-Hill, New York, 1956)

[2] C.W.J. Granger, Econometrica 37 (1969) 424

[3] K. Hlavackova-Schindler et al., Phys. Rep. 441 (2007) 1

[4] M. Palus, M. Vejmelka, Phys. Rev. E 75 (2007) 056211

[5] J. Runge et al., Nature Communications 6 (2015) 8502

[6] M. Palus, Phys. Rev. Lett. 112 (2014) 078702

[7] N. Jajcay, J. Hlinka, S. Kravtsov, A. A. Tsonis, M. Palus, Geophys. Res. Lett. 43(2) (2016) 902-909

11:55–12:10 Norbert Marwan, Tobias Braun, K. Hauke Kraemer, Abhirup Banerjee, Deniz Eroglu Recurrence plots for analysing extreme events data
The analysis of time series of extreme events such as heat waves, tropical cyclones, or floods is challenging due to the heavy-tailed distribution, irregular occurrence of events and their sparsity. Traditional (linear) data analysis tools, in general, fail to tackle many research questions based on extreme events, such as synchronisation analysis or power spectrum estimation of extreme event data. We demonstrate some recent extensions of the (nonlinear) recurrence plot approach for various applications in the field of extreme events data. We demonstrate their potential for synchronisation analysis between signals of extreme events and signals with continuous and slower variations, for estimation of power spectra of spiky signals, and for analysing data with irregular sampling.

12:10–12:25 Noémie Ehstand A percolation framework to anticipate fast changes in irregular climate oscillations
Functional networks are powerful tools to investigate the structure and dynamics of complex systems. Rodriguez-Mendez et al.~(2016) showed that percolation properties of correlation networks provide very early-warning indicators for bifurcation-induced tipping in several model systems. Further, they showed that the same quantities in correlation networks of observed sea surface temperatures could be used to anticipate El N\~no and La Ni\~na events. In this later case however, the question of which mechanisms generate the percolation transitions remains open.
Here, we study the percolation properties of correlation networks in spatially-extended, irregularly-oscillating systems. In particular, we consider a system of coupled stochastic Fitzhugh-Nagumo oscillators and show that the percolation measures anticipate the (sharp) transitions between different stages of the oscillation. Unveiling the mechanisms which cause the percolation transitions in this system leads to a better understanding and interpretation of the outcomes of the percolation-framework when applied to the El Ni\~no-Southern Oscillation.

This research was conducted as part of the CAFE Innovative Training Network which has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 813844.

12:25–12:30 Jakob Runge, Bruno Merz Wrap-up

MS 9 – Tipping points

Convener: Niklas Boers, Valerio Lucarini
Room: lecture room 1

Friday, March 17th, 14:00–15:30

14:00–14:18 N. Sharafi, C. Martin, S. Hallerberg Critical Transitions and Perturbation Growth
Critical transitions occur in a variety of dynamical systems. Here we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for critical transitions, we consider changes in growth rates and directions of covariant Lyapunov vectors. Studying critical transitions in several models of fast-slow systems, i.e., a network of coupled FitzHugh-Nagumo oscillators, models for Josephson junctions, and the Hindmarsh-Rose model, we find that tangencies between covariant Lyapunov vectors are a common and maybe generic feature during critical transitions. Additionally, we present an approach to estimate covariant Lyapunov vectors from data and another approach to calculate approximations of covariant Lyapunov vectors without using the far future of a data-record.

14:18–14:36 Keno Riechers, Georg Gottwald, Niklas Boers Glacial abrupt climate change as a multi-scale phenomenon resulting from monostable excitable dynamics
Paleoclimate proxy records evidence repeated abrupt climatic transitions during past glacial intervals with strongest expression in the North Atlantic region. Temperature reconstructions from Greenland ice cores reveal sudden high northern latitude warming events of up to 16{\textdegree}C on decadal time scales, but associated impacts extend across the globe, including disruptions of the tropical monsoon systems and temperature variations in Antarctica. Do we need this specification here? These so-called Dansgaard-Oeschger (DO) events are commonly considered as the archetype of past abrupt climate changes.

In Greenland ice core records the DO warming events are followed by phases of relatively mild temperatures termed Interstadials, which exhibit gradual cooling prior to a final phase of abrupt temperature decrease back to cold Stadials. To date, there is no consensus about the origin of this millennial-scale variability. Here, we propose an excitable model to explain the DO cycles, in which Interstadials are regarded as noise-induced state space excursions of an excitable system. Our model comprises the mutual multi-scale interactions between four dynamical variables representing Arctic atmospheric temperatures, Nordic Seas’ temperatures and sea ice cover, and the Atlantic Meridional Overturning Circulation (AMOC). Crucially, the model’s atmosphere-ocean heat flux is moderated by the sea ice variable which in turn is subject to large perturbations dynamically generated by a fast evolving intermittent noise process. These perturbations, which we suggest to originate from convective events in the ocean or atmospheric blocking events, may trigger Interstadial-like state space excursion seizing all four model variables. The key characteristics of DO cycles are reproduced by our model with remarkable resemblance to the proxy record; in particular, their shape, return time, as well as the dependence of the Interstadial and Stadial durations on the background temperatures are reproduced accurately. In contrast to the prevailing understanding that the DO variability showcases bistability in the underlying dynamics, we conclude that multi-scale, monostable excitable dynamics provides a promising alternative candidate to explain the millennial-scale climate variability associated with the DO events.

14:36–14:54 Martin Hessler, Oliver Kamps Bayesian on-line anticipation of critical transitions
The design of reliable indicators to anticipate critical transitions in complex systems is an important task in order to detect imminent regime shifts and to intervene at an early stage to either prevent them or mitigate their consequences. We present a data-driven method based on the estimation of a parameterized nonlinear stochastic differential equation that allows for a robust anticipation of critical transitions even in the presence of strong noise which is a characteristic of many real world systems. Since the parameter estimation is done by a Markov chain Monte Carlo approach, we have access to credibility bands allowing for a better interpretation of the reliability of the results. We also show that the method can yield meaningful results under correlated noise. By introducing a Bayesian linear segment fit it is possible to give an estimate for the time horizon in which the transition will probably occur based on the current state of information. This approach is also able to handle nonlinear time dependencies of the parameter that controls the transition. The method can be used as a tool for on-line analysis to detect changes in the resilience of the system and to provide information on the probability of the occurrence of critical transitions in future. Additionally, it can give valuable information about the possibility of noise induced transitions. The discussed methods are made easily accessible via a flexibly adaptable open source toolkit named ‘antiCPy’ which is implemented in the programming language Python.

14:54–15:12 Induja Pavithran, P. R. Midhun, R.I. Sujith Tipping in complex systems under fast variations of parameters
Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally demonstrate rate-induced tipping in a real-world complex system, namely a turbulent reactive flow system, and decipher its mechanism. The system exhibits tipping to a dangerously high amplitude oscillatory state known as thermoacoustic instability. We continuously vary a control parameter driving the system towards conditions favorable for an alternative stable state, i.e., thermoacoustic instability (stable limit cycle oscillations). We find that the wall temperature is a slow variable that varies simultaneously at a different timescale, increasing the damping of oscillations in the system variables. The competition between the effects of these different timescales determines if and when tipping occurs. There is a critical rate of change of control parameter above which the system undergoes tipping. Motivated by the experiments, we use a nonlinear oscillator model exhibiting Hopf bifurcation to generalize this tipping to complex systems where the competition between the slow and fast timescales determines the dynamics.

15:12–15:30 Frank Kwasniok Data-driven anticipation and prediction of Atlantic Meridional Overturning Circulation collapse using non-autonomous spatiotemporal dynamical modelling
A data-driven methodology for identifying, anticipating and predicting critical transitions in high-dimensional model or observational data sets is introduced, based on explicit non-autonomous modelling of the tipping dynamics. Unlike the more traditional early-warning signs, this allows for dynamical understanding of the underlying tipping mechanism and genuine prediction of the future system state by extrapolation. A set of spatial modes carrying the tipping dynamics are identified and a nonlinear stochastic model of appropriate complexity is estimated in the subspace spanned by these modes. Analysis of the reconstructed dynamics allows to determine the type of the impending bifurcation. Different competing tipping mechanisms can be compared and assessed using likelihood inference and information criteria. The methodology is here applied to a data set from a climate model simulation of Atlantic Meridional Overturning Circulation (AMOC) collapse, actually a freshwater hosing experiment with the FAMOUS GCM. The AMOC on-state is found to lose stability via a subcritical Hopf bifurcation; however, the transition to the off-state occurs far ahead of reaching the bifurcation point. The early collapse can be explained by a combination of rate-induced and noise-induced tipping.