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.

中文翻译：

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两个耦合的相同 Hindmarsh 中的混沌和超混沌 – Rose Systems

摘要

研究了两个耦合神经元模型 Hindmarsh-Rose 系统的动力学。它们的相互作用是通过化学耦合来模拟的，该化学耦合是用 sigmoid 函数实现的。结果表明，该模型可能表现出复杂的行为：准周期、混沌和超混沌振荡。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场景。结果表明，这些吸引子的形成导致同相突发振荡的出现。