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Regular and Chaotic Dynamics, 2024, Volume 29, Issue 1, paper published in the English version journal
DOI: https://doi.org/10.1134/S1560354724010131
(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
Citations (1)
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Abstract: 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.
Keywords: chaos, heteroclinic cycle, weak chimera
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FSRW-2020-0036
Russian Science Foundation 22-12-00348
This work was supported by the Ministry of Science and Education of the Russian Federation, Contract no. FSRW-2020-0036 (A.E.E. and E.A.G.) and RSF grant 22-12-00348 (T.A.L.).
Received: 31.08.2023
Accepted: 12.01.2024
Bibliographic databases:
Document Type: Article
MSC: 65P20
Language: English
Citation: Artyom E. Emelin, Evgeny A. Grines, Tatiana A. Levanova
Citation in format AMSBIB
\Bibitem{EmeGriLev24}
\by Artyom E. Emelin, Evgeny A. Grines, Tatiana A. Levanova
\mathnet{http://mi.mathnet.ru/rcd1254}
\crossref{https://doi.org/10.1134/S1560354724010131}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4716365}
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    References:17
     
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