Reviews of topical problems

Spatio-temporal structures in ensembles of coupled chaotic systems

Physics Department, Saratov State University named after N.G. Chernyshevsky, ul. Astrakhanskaya 83, Saratov, 410012, Russian Federation

We present a review of numerical results of studies of the complex dynamics of one- and two-dimensional networks (ensembles) of nonlocally coupled identical chaotic oscillators in the form of discrete- and continuous-time systems, as well as lattices of coupled ensembles. We show that these complex networks can demonstrate specific types of spatio-temporal patterns in the form of chimera state. The latter is known as the coexistence of spatially localized domains of coherent (synchronized) and incoherent (asynchronous) dynamics in a network of nonlocally coupled identical oscillators. In the review phase, amplitude, double-well chimeras and solitary states are described and their basic characteristics are analyzed and compared. We focus on two basic discrete-time models, the Henon and Lozi maps, which can be used to describe the typical chimera structures and solitary states in networks of a wide range of chaotic oscillators. We discuss the bifurcation mechanisms of their appearance and evolution. In conclusion, we describe effects of synchronization of chimera states in coupled ensembles of chaotic maps.

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Keywords: ensembles, nonlocal coupling, chimera states, spatio-temporal structure, synchronization, discrete maps, dynamical chaos
PACS: 05.45.Ra, 05.45.Xt, 05.65.+b (all)
DOI: 10.3367/UFNe.2019.01.038518
Citation: Strelkova G I, Anishchenko V S "Spatio-temporal structures in ensembles of coupled chaotic systems" Phys. Usp. 63 145–161 (2020)
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Received: 10th, October 2018, revised: 10th, January 2019, 17th, January 2019

Оригинал: Стрелкова Г И, Анищенко В С «Пространственно-временные структуры в ансамблях связанных хаотических систем» УФН 190 160–178 (2020); DOI: 10.3367/UFNr.2019.01.038518

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