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.
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).
\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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This publication is cited in the following 4 articles:
Nikita Barabash, Igor Belykh, Alexey Kazakov, Michael Malkin, Vladimir Nekorkin, Dmitry Turaev, “In Honor of Sergey Gonchenko and Vladimir Belykh”, Regul. Chaotic Dyn., 29:1 (2024), 1–5
S. Serrano, R. Barrio, Á. Lozano, A. Mayora-Cebollero, R. Vigara, “Coupling of neurons favors the bursting behavior and the predominance of the tripod gait”, Chaos, Solitons & Fractals, 184 (2024), 114928
Efrosiniia Karatetskaia, Vladislav Koryakin, Konstantin Soldatkin, Alexey Kazakov, “Routes to Chaos in a Three-Dimensional Cancer Model”, Regul. Chaotic Dyn., 29:5 (2024), 777–793
R. Prabu, P. Dhinakar, S. Prakash, N. Gayathri, 2024 3rd Edition of IEEE Delhi Section Flagship Conference (DELCON), 2024, 1
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