时滞作用下忆阻耦合FHN-ML神经元模型的分岔分析

通过构建时滞作用下忆阻耦合FHN-ML神经元模型，研究不同时滞对该神经元系统动力学行为的影响。利用Routh-Hurwitz判据和Hopf分岔定理证明FHN-ML神经元系统平衡点的稳定性及Hopf分岔的存在性。利用范式理论和中心流形定理进一步证明FHN-ML神经元系统的分岔方向及周期解的稳定性。通过Matlab软件绘制以反转电压和电流频率为双参的周期分岔图及以电流频率为单参的峰峰间期（ISI）分岔图，发现在时滞作用下，FHN-ML神经元系统的放电模式会产生延迟现象，且当增大时滞时，延迟程度加大，混沌放电区域减小，加周期分岔的周期数减小。所得分析结果有助于理解延迟效应对电磁辐射作用下的耦合神经元网络放电活动的影响。

Bifurcation analysis of memristor-coupled FHN-ML neuron model with time delay

Abstract: A model of memristor-coupled FHN-ML neurons with time delay is constructed to investigate the effects of different time delays on the dynamic behavior of the neuron system. The stability of the equilibrium point and the existence of the Hopf bifurcation in FHN-ML neuron system are proved by Routh-Hurwitz criterion and Hopf bifurcation theorem. The bifurcation direction and the stability of periodic solution of FHN-ML neural system are further proved by paradigm theory and center manifold theorem. The periodic bifurcation diagrams with reverse voltage and current frequency as two parameters and the inter-spike interval bifurcation diagrams with current frequency as single parameter are drawn by MATLAB software, and it is found that under the effect of time delay, the firing pattern of FHN-ML neuron system produces a delay phenomenon. With the increasing of time delay, the degree of delay increases, and the chaotic firing area decreases, and the number of periods with periodic bifurcation decreases. The results are helpful to understand the effect of delay effect on the firing activity of the coupled neural network under electromagnetic radiation exposures.