Izvestiya of Saratov University.


ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

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Bukh A. V., Kosenkova A. S., Anishchenko V. S. Reflecting, Nonlocal, and Diagonal Coupling Topologies in Networks of the Coupled Dynamics Elements with Various Nature. Izvestiya of Saratov University. Physics , 2020, vol. 20, iss. 1, pp. 16-28. DOI: 10.18500/1817-3020-2020-20-1-16-28

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Reflecting, Nonlocal, and Diagonal Coupling Topologies in Networks of the Coupled Dynamics Elements with Various Nature

Bukh Andrey Vladimirovich, Saratov State University
Kosenkova Anastasia Sergeevna, Saratov State University
Anishchenko Vadim Semenovich, Saratov State University

Backgrounds and Objectives: Networks of coupled dynamical o scillators are of high interest for last decades. The interest to their dynamics greatly increases with the discovery of chimera states. The latter are characterized by the coexistence of regions with coherent and incoherent behavior. There are many works devoted to the networks with nonlocal coupling topology, but the influence of the coupling topology type has not been sufficiently studied. In this paper we consider recently proposed reflecting and diagonal topologies of coupling and compare them with the nonlocal coupling. The issue addressed in the paper is of great interest and importance because of the topological correspondence to biological neuron networks. Logistic maps, FitzHugh-Nagumo oscillators, and Courbage-Nekorkin models are selected as partial subsystems in networks. Materials and Methods: The numerical analysis is carried out using a program complex in C++ which was developed for modeling dynamical systems with different topologies of coupling. Snapshots of amplitudes of oscillators and spatio-temporal diagrams are used to diagnose the dynamical regimes. Results: Numerical results have shown that a number of incoherent areas of chimera states varies when the coupling topology changes. In addition, the features of the transition from the incoherence regime to the completely synchronized state with increasing coupling strength depend on the choice of coupling topology. It is shown that a certain type of waves, namely, traveling waves, cannot be realized in the case of reflecting coupling. Conclusion: The performed studies have indicated that the coupling topology can affect the behavior of the networks. There is a possibility to obtain different regimes by choosing different topologies of coupling. Herewith, the coupling strength value for chimera states is preserved as the coupling topology changes.

Работа выполнена при финансовой поддержке Немецкого Физического Общества (проект 163436311-SFB 910). В.С.А. благодарит за финансовую поддержку РФФИ и DFG (проект №20-52-12004, получение результатов, написание текста). А.В.Б. благодарит за финансовую поддержку РФФИ (проект № 19-32-90005, анализ результатов).
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