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JOURNALS // Regular and Chaotic Dynamics // Archive

Regul. Chaotic Dyn., 2024 Volume 29, Issue 1, Pages 120–133 (Mi rcd1248)

This article is cited in 2 papers

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

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

MSC: 65P20, 92B25

Received: 28.04.2023
Accepted: 10.10.2023

Language: English

DOI: 10.1134/S1560354723540031



© Steklov Math. Inst. of RAS, 2024