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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/S1560354723540031 (Mi rcd1248) 		 
This article is cited in 1 scientific paper (total in 2 paper)

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

Chaos and Hyperchaos in Two Coupled Identical Hindmarsh – Rose Systems

Nataliya V. Stankevich, Andrey A. Bobrovskii, Natalya A. Shchegoleva

HSE University, ul. Bolshaya Pecherskaya 25/12, 603155 Nizhny Novgorod, Russia
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DOI: https://doi.org/10.1134/S1560354723540031
Abstract: The dynamics of two coupled neuron models, the Hindmarsh – Rose systems, are studied. Their interaction is simulated via a chemical coupling that is implemented with a sigmoid function. It is shown that the model may exhibit complex behavior: quasi- periodic, chaotic and hyperchaotic oscillations. A phenomenological scenario for the formation of hyperchaos associated with the appearance of a discrete Shilnikov attractor is described. It is shown that the formation of these attractors leads to the appearance of in-phase bursting oscillations.
Keywords: neuron model, Hindmarsh – Rose system, chaos, hyperchaos, in-phase bursting
Funding agency Grant number
Russian Science Foundation 20-71-10048
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-1101
This work is supported by the Russian Science Foundation (project no. 20-71-10048, Sections 2.2, 3, 5). NVS, AAB are partially supported by the Laboratory of Dynamical Systems and Applications NRU HSE, grant of the Ministry of Science and Higher Education of the RF, ag. no. 075-15-2022-1101 (Sections 2.1, 4).
Received: 28.04.2023
Accepted: 10.10.2023
Document Type: Article
MSC: 65P20, 92B25
Language: English
Citation: Nataliya V. Stankevich, Andrey A. Bobrovskii, Natalya A. Shchegoleva
Citation in format AMSBIB
\Bibitem{StaBobShc24}
\by Nataliya V. Stankevich, Andrey A. Bobrovskii, Natalya A. Shchegoleva
\mathnet{http://mi.mathnet.ru/rcd1248}
\crossref{https://doi.org/10.1134/S1560354723540031}
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