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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2024, том 29, выпуск 1, страницы 205–217 (Mi rcd1254)

Special Issue: In Honor of Vladimir Belykh and Sergey Gonchenko Guest Editors: Alexey Kazakov, Vladimir Nekorkin, and Dmitry Turaev

Chaos in Coupled Heteroclinic Cycles Between Weak Chimeras

Artyom E. Emelin, Evgeny A. Grines, Tatiana A. Levanova

Lobachevsky University, pr. Gagarin 23, 603022 Nizhny Novgorod, Russia

Аннотация: Heteroclinic cycles are widely used in neuroscience in order to mathematically describe different mechanisms of functioning of the brain and nervous system. Heteroclinic cycles and interactions between them can be a source of different types of nontrivial dynamics. For instance, as it was shown earlier, chaotic dynamics can appear as a result of interaction via diffusive couplings between two stable heteroclinic cycles between saddle equilibria. We go beyond these findings by considering two coupled stable heteroclinic cycles rotating in opposite directions between weak chimeras. Such an ensemble can be mathematically described by a system of six phase equations. Using two-parameter bifurcation analysis, we investigate the scenarios of emergence and destruction of chaotic dynamics in the system under study.

Ключевые слова: chaos, heteroclinic cycle, weak chimera

MSC: 65P20

Поступила в редакцию: 31.08.2023
Принята в печать: 12.01.2024

Язык публикации: английский

DOI: 10.1134/S1560354724010131



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