Hindmarsh-Rose神经元网络的同步稳定性分析

Synchronization and Stability of Hindmarsh-Rose Neuronal Network

摘要: 本文分析了Hindmarsh-Rose (HR)神经元的脉冲放电和簇放电行为，我们引进脉冲宽度比来描述外界激励电流对神经元放电模式的影响，并给出HR神经元从簇放电到连续脉冲转变的临界值，我们发现控制参数μ可以用来控制簇放电中连续脉冲的数目。另外，我们应用主稳定性函数的方法分析HR神经元网络的同步稳定性，发现神经元网络的同步稳定性依赖于网络的耦合强度和网络结构，对神经元的放电模式并不敏感。当外界激励电流使网络同步不稳定时，增大μ对网络同步稳定有好处。我们给出HR神经元网络同步稳定性在神经元参数和网络参数空间中的相图。

Abstract: We analyze numerically the neuronal activity of bursting and spiking in the 3D Hindmarsh-Rose (HR) neuronal model. We introduce the ratio of different pulse to give the critical current I, which induces the continuous bursting behavior of neuron. We find that the parameter μ can control the number of peaks in a discharge cycle. Moreover, we numerically investigate the synchronization and stability of linear coupling HR neuronal network by the master function method. We find that the synchronization and its stability depend on the coupling strength and the structure of the network, but weakly related to the bursting and spiking phenomena. We give the phase diagram of the synchronization and its stability of the HR neuronal network in the parameter space, which provides an understanding of the dynamic behavior and its stability of HR neuronal network.