
chair: Christoph Bruder

09:00  09:45

Anna Zakharova
(Technische Universität Berlin)
Chimera states in multilayer networks
Multilayer networks offer a better representation of the topology and dynamics of realworld systems in comparison with isolated onelayer structures. The prime objective of multilayer networks is to explore multiple levels of interactions where functions of one layer get affected by the properties of other layers. One of the most promising applications of the multilayer approach is the study of the brain, or technological interdependent systems, i.e., those systems in which the correct functioning of one of them strongly depends on the status of the others. Multiplexing plays an important role in controlling since it is not always possible to directly access and manipulate the desired layer, while the network it is multiplexed with may be adaptable. We investigate multilayer networks of coupled FitzHughNagumo neurons and focus on the case of weak multiplexing, i.e., when the coupling between the layers is smaller than that inside the layers. It turns out that weak multiplexing has an essential impact on the dynamical patterns observed in the system and can be used for controlling in both oscillatory and excitable regimes. In the oscillatory regime, we show that different types of partial synchronization patterns such as chimera states [12] and solitary states [34] can be induced and suppressed. In the excitable regime with noise, we find that weak multiplexing induces coherence resonance in networks that do not demonstrate this phenomenon in isolation [5].
[1] A. Zakharova, Chimera Patterns in Networks: Interplay between Dynamics, Structure, Noise, and Delay, Understanding Complex Systems, Springer, ISBN 9783030217136, (2020)
[2] M. Mikhaylenko, L. Ramlow, S. Jalan, and A. Zakharova, Weak multiplexing in neural networks: Switching between chimera and solitary states, Chaos 29, 023122 (2019)
[3] E. Rybalova, V. S. Anishchenko, G. I. Strelkova, A. Zakharova,
Solitary states and solitary state chimera in neural networks, Chaos Fast Track 29, 071106 (2019)
[4] L. Schülen, S. Ghosh, A. D. Kachhvah, A. Zakharova, S. Jalan,
Delay engineered solitary states in complex networks, Chaos, Solitons and Fractals 128, 290 (2019)
[5] N. Semenova, A. Zakharova, Weak multiplexing induces coherence resonance, Chaos 28, 051104 (2018) *Selected as Editor’s Pick

09:45  10:30

Igor Belykh
(Georgia State University, Atlanta)
Stability of rotatory solitary states in Kuramoto networks with inertia
Solitary states emerge in oscillator networks when one oscillator separates from the fully synchronized cluster and oscillates with a different frequency. Such chimeratype patterns with an incoherent state formed by a single oscillator were observed in various oscillator networks; however, there is still a lack of understanding of how such states can stably appear. Here, we study the stability of solitary states in Kuramoto networks of identical twodimensional phase oscillators with inertia and a phaselagged coupling. The presence of inertia can induce rotatory dynamics of the phase difference between the solitary oscillator and the coherent cluster. We derive asymptotic stability conditions for such a solitary state as a function of inertia, network size, and phase lag that
may yield either attractive or repulsive coupling. Counterintuitively, our analysis demonstrates that (1) increasing the size of the coherent cluster can promote the stability of the solitary state in the attractive coupling case and
(2) the solitary state can be stable in smallsize networks with all repulsive coupling. We also discuss the implications of our stability analysis for the emergence of rotatory chimeras. This is a joint work with V. Munyayev,
M. Bolotov , L. Smirnov, and G. Osipov.

10:30  11:00

Coffee break

11:00  11:45

Victor M. Bastidas
(NTT Basic Research Laboratories)
Chimera states in Nonequilibrium quantum Manybody Systems

11:45  12:30

HonWai Hana Lau
(Nanyang Technological University Singapore)
Chimeras patterns in conservative systems and the implementation in ultracold atoms
Chimera states, characterized by coexisting regions of phase coherence and incoherence, are stable patterns even in a system with translational and rotational symmetry. Its existence has been experimentally demonstrated in chemical, mechanical, electronic, and optoelectronic systems. Here, we show
the formation of chimera patterns should also be observable in ultracold atoms. More generally, chimera patterns exists in conservative Hamiltonian systems with longrange nonlocal hopping in which both energy and particle number are conserved. In particular, we outline the implementation in a twocomponent BoseEinstein condensate with a spindependent optical lattice. The calculated parameter regime are well within the current implementable technology.

12:30  13:30

Lunch break

13:30  13:55

Discussions


chair: Anna Zakharova

13:55  14:00

Group photo (virtual and onsite audience)

14:00  14:45

Adilson Motter
(Northwestern University, Evanston)
A Mechanism for the Emergence of Chimera States (virtual)
Chimera states have attracted significant attention as symmetrybroken states exhibiting the coexistence of coherence and incoherence. Despite the valuable insights gained by analyzing specific systems, the understanding of the physical mechanism underlying the emergence of chimeras has been incomplete. In this presentation, I will argue that an important class of stable chimeras arise because coherence in part of the system is sustained by incoherence in the rest of the system. This mechanism may be regarded as a deterministic analog of noiseinduced synchronization and is shown to underlie the emergence of socalled strong chimeras. These are chimera states whose coherent domain is formed by identically synchronized oscillators. The link between coherence and incoherence revealed by this mechanism also offers insights into the dynamics of a broader class of states, including switching chimera states.
References: Y. Zhang and A. E. Motter, Mechanism for strong chimeras, Phys. Rev. Lett. 126, 094101 (2021); Y. Zhang, Z. G. Nicolaou, J. D. Hart, R. Roy, and A. E. Motter, Critical switching in globally attractive chimeras, Phys. Rev. X 10, 011044 (2020).

14:45  15:10

Oleh Omel'chenko
(University of Potsdam)
Chimera states that breathe and move
Systems of nonlocally coupled oscillators have been the subject of much research over the past decades. It has been found that in many cases they support complex spatiotemporal patterns of coexisting coherence and incoherence, called chimera states. Until now, such chimera states have been studied mostly in the stationary case, when the shape and position of the chimera pattern remain unchanged over time. Nonstationary coherenceincoherence patterns, in particular periodically breathing or moving chimera states, were also reported, however not investigated systematically because of their complexity. In this talk, we report a number of theoretical results related to the latter nonstationary patterns. In particular, we show typical bifurcation diagrams that mediate their appearance and reveal the constructive role of oscillator heterogeneities for the stability of these patterns.

15:10  15:35

Géza Ódor
(Centre for Energy Research Budapest)
Frustrated synchronziation in powergrid and brain models
Due to heterogeneity Kuramoto models exhibit frustrated synchronization around
the synchronization transition. Powergrids can be described by the second order
Kuramoto model. I provide numerical evidence for an extended coupling region, where blackout cascade size distribution exhibit exhibit powerlaw tails and show the spatial structure of the local Kuramoto order parameter [1,2]
For modelling the brain the first order Kuramoto serves as a simplest oscillatory model. On heterogenous, modular connectome graphs we can find extended dynamical
critical region with large steady state fluctuations as compared to random graphs
[3,4,5]. We show new results for the local Kuramto maps on connectomes.
[1] Géza Ódor and Bálint Hartmann, Heterogeneity effects in power grid network models, Phys. Rev. E 98 (2018) 022305
[2] Géza Ódor and Bálint Hartmann, PowerLaw Distributions of Dynamic Cascade Failures in PowerGrid Models Entropy 22 (2020) 666
[3] Géza Ódor and Jeffrey Kelling, Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs, Scientific Reports 9 (2019) 19621
[4] Géza Ódor, Jeffrey Kelling and Gustavo Deco, The effect of noise on the synchronization dynamics of the Kuramoto model on a large human connectome graph
Neurocomputing, 461 (2021) 696704.
[5] Géza Ódor, Gustavo Deco and Jeffrey Kelling, What makes us humans: Differences in the critical dynamics underlying the human and fruitfly connectome
arXiv:2201.11084, acceptrd in Phys. Rev. Res.

15:35  16:00

Rico Berner
(HumboldtUniversity zu Berlin)
Emergence of partial synchronization in adaptive oscillator networks
Recently, a new phenomenon, called solitary state, in the transition from incoherence to complete coherence was discovered. We analyze networks of adaptively coupled phase oscillators and observe a variety of frequencysynchronized states including solitary states. Despite the fact that solitary states have been observed in a plethora of dynamical systems, the mechanisms behind their emergence were largely unaddressed in the literature. Here, we show how solitary states and other partial synchronization patterns emerge due to the adaptive feature of the network. By using numerical and analytical methods, we classify several bifurcation scenarios in which these states are created and stabilized.

16:00  16:30

Coffee break


chair: István Z. Kiss

16:30  16:55

Patrycja Jaros
(Lodz University of Technology)
Complex dynamics of small chimera states
In everyday speech the word ‘chimera’ is used to describe objects composed of inharmonious parts. In the field of dynamical systems there exist a term "weak chimera state", which is defined by at least one oscillator rotating with a different average frequency in comparison to at least two others, which are frequency synchronized.
When coupling small number of phase oscillators with inertia, weak chimera states can be obtained. They are present in the form of inphase, antiphase or rotating wave chimeras. Each of these chimeras may occur as one of its permutations.
Parameter regions of the stable chimera states are surrounded by the socalled riddling shadow, where the network behavior represents heteroclinic switching between multiple saddle chimera states (i.e. permutationally different chimeras). Basins of the chimeras are riddled, what cause extreme sensitivity of the switching solutions to initial conditions and the parameters.
Another strange puzzle is induced by a presumable presence of antipodal points or other chimera states as the switching trajectories then can tend to one of them. The dynamics becomes hardly predictable.

16:55  17:20

Andrey Shilnikov
(Georgia State University, Atlanta)
Computational exposition of multistable rhythms in 4cell neural circuits
The coexistence of multistable rhythms generated by oscillatory neural circuits made up of 4 and more cells, their onset, stability conditions, and the transitions between such rhythms are not well understood. This is partly due to the lack of appropriate visual and computational tools. In this study, we employ modern computational approaches including unsupervised machine learning (clustering) algorithms and fast parallel simulations powered by graphics processing units (GPUs) to further extend our previously developed techniques based on the theory of dynamical systems and bifurcations. This allows us to analyze the fundamental principles and mechanisms that ensure the robustness and multifunctionality of such neural circuits. In addition, we examine how network topology affects the dynamics, and the rhythmic patterns transition/bifurcate as network configurations are altered and the intrinsic properties of the cells and the synapses are varied. This study elaborates on a set of inhibitory coupled 4cell circuits that can exhibit a variety of mono and multistable rhythms including pacemakers, paired halfcenters, traveling waves, synchronized states, as well as various chimera states which are characterized by two subpopulations firing at distinct frequencies.. Our detailed analysis is helpful to generate verifiable hypotheses for neurophysiological experiments with biological central pattern generators.
Krishna Pusuluri, Sunitha Basodi, Andrey Shilnikov
Neuroscience Institute
Georgia State University USA

17:20  17:45

Pezhman Ebrahimzadeh
(Forschungszentrum Jülich)
Mix mode chimera states in network of pendula
We report the emergence of chimera states as frequency clusters in the network of identical pendulua with phaselag coupling. Such clusters include multiple rotation mode pendulums, where average frequencies are nonzero, and an oscillation mode cluster with zero average frequency. The dynamics of each cluster lies on a synchronization manifold with mixed mode oscillations. The formation of mix mode chimeras are studied in detail for the minimal network of only $N=3$ pendulums. Parameter region for the coexistence of different combinations of the mix mode chimera states are obtained and the dependence on the initial conditions are shown through the multiple basins of attraction. The analysis suggests that the robust mixed mode chimera states can commonly characterize the complex dynamics of diverse pendulalike systems widespread in the nature.

17:45  18:10

Michael Rosenblum
(University of Potsdam)
Highorder phase reduction applied to remote synchronization
We discuss the analytical and numerical approaches to phase reduction in networks of coupled oscillators in the higher orders of the coupling parameter. Particularly, for three coupled Stuart–Landau (SL) oscillators, where the phase can be introduced explicitly, an analytic perturbation procedure yields the explicit secondorder approximation [1]. We exploit the analytical result from [1] to analyze the mechanism of the remote synchronization (RS). RS, briefly reported by Okuda and Kuramoto as early as 1991, implies that oscillators interacting not directly but via an additional unit (hub) adjust their frequencies and exhibit frequency locking while the hub remains asynchronous. Previous studies uncovered the role of amplitude dynamics and of nonisochronicity: RS appeared in a network of isochronous SL units but not in its firstorder phase approximation, the Kuramoto network. Furthermore, RS emerged in networks of phase oscillators with the KuramotoSakaguchi interaction, but not in the case of zero phase shift in the sinecoupling term; this result indicates the role of nonisochronicity. In this work, 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 secondorder phase approximation. We explain the contribution of both factors and quantitatively describe the transition to RS. We demonstrated that the RS transition is determined by the interplay of the nonisochronicity and the amplitude dynamics. The impact of the latter factor renders the standard firstorder phase dynamics descripion of the RS phenomenon invalid. Our result emphasizes the importance of higherorder phase reduction and highlights the crucial role amplitude dynamics may have in governing the behavior of networks of nonlinear oscillators. We show a good correspondence between our theory and numerical results for small and moderate coupling strengths and argue that the effect of the amplitude dynamics neglected in the firstorder phase approximation and revealed by the higherorder one holds for general limitcycle oscillators.
[1] E. Gengel, E. Teichmann, M. Rosenblum, and A. Pikovsky, J. of Physics: Complexity, 2, 015005 (2021)
[2] M. Kumar and M. Rosenblum, PRE 104, 054202 (2021)

18:15  19:15

Dinner

19:15  20:15

Poster Session (onsite; main building, 2nd floor)

20:15  21:15

Poster Session (virtual via gather.town)
