Abstract

Memristor synapse can be used to characterize the electromagnetic induction effect between two neurons that induces an action current by their membrane potential difference. This paper proposes a memristor synapse-coupled neuron network with no equilibrium, which is achieved using a memristor synapse to connect the membrane potentials of two identical three-dimensional memristive Hindmarsh–Rose neurons. Exponential synchronization is proved theoretically, and synchronous activities are discussed numerically. The theoretical and numerical results illustrate that the synchronicities of memristor synapse-coupled neuron network are related to the memristor coupling coefficient and especially related to the initial states of memristor synapse and coupling neurons. Furthermore, by constructing a ring network of memristor synapse-coupled neuron network, several types of collective behaviors including incoherent, coherent, imperfect synchronization, and chimera states are disclosed numerically, which indicate that the chimera states arisen in the ring network are dependent on the memristor coupling coefficient and sub-network coupling strength.

中文翻译：

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忆阻器突触耦合忆阻神经元网络：同步过渡和嵌合体的发生。

摘要

忆阻器突触可用于表征两个神经元之间的电磁感应效应，该感应效应通过其膜电位差来感应动作电流。本文提出了一种不平衡的忆阻器突触耦合神经元网络，它是通过忆阻器突触连接两个相同的三维忆阻性Hindmarsh-Rose神经元的膜电位来实现的。从理论上证明了指数同步，并通过数值讨论了同步活动。理论和数值结果表明，忆阻器突触耦合神经元网络的同步性与忆阻器耦合系数有关，尤其与忆阻器突触和耦合神经元的初始状态有关。此外，通过构建忆阻器突触耦合神经元网络的环形网络，