Regular and Chaotic Dynamics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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
(1)
References:
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}
Linking options:
  • https://www.mathnet.ru/eng/rcd1254
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:24
    References:16
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024