Chaos and Hyperchaos in Two Coupled Identical Hindmarsh – Rose Systems

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2023-12-19 DOI:10.1134/S1560354723540031

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

引用次数: 0

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.

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两个完全相同的辛德马什-罗斯耦合系统中的混沌与超混沌

摘要研究了两个耦合神经元模型（Hindmarsh - Rose 系统）的动力学。它们之间的相互作用是通过化学耦合来模拟的，而化学耦合是用一个 sigmoid 函数来实现的。结果表明，该模型可能表现出复杂的行为：准周期振荡、混沌振荡和超混沌振荡。描述了与离散希尔尼科夫吸引子的出现相关的超混沌形成的现象学情景。研究表明，这些吸引子的形成会导致同相猝发振荡的出现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.