双忆阻Chay神经元系统分岔与同步转迁特性分析

Analysis of Bifurcation and Synchronization Transition Characteristics of Dual-Memristor Chay Neuron System

摘要: 本文以忆阻Chay神经元作为研究对象，采用电学突触构建双忆阻神经元耦合系统，研究不同参数条件下耦合系统的放电模式、分岔类型与同步转迁规律。利用四阶变步长Runge-Kutta算法对系统方程进行数值求解，绘制峰峰间期分岔图研究系统的放电节律随参数的演化过程，得出耦合系统会出现逆加周期分岔、边界激变分岔、吸引子合并激变及逆倍周期分岔等多种典型分岔类型，且放电模式由簇放电转变为尖峰放电。研究电耦合强度对耦合系统完全同步状态的影响，得出电耦合强度是决定系统能否进入完全同步状态的主导因素，且耦合强度越大，完全同步状态所占的参数区域越大。研究忆阻神经元系统分岔与同步状态可揭示不同参数值对耦合系统放电节律的影响，也为生物神经性疾病的治疗提供理论参考。

Abstract: In this paper, the memristive Chay neuron is taken as the research object, and a coupled system of two memristive neurons is constructed by using electrical synapses. The firing patterns, bifurcation types, and synchronization transition laws of the coupled system are investigated under different parameter conditions. The system equations are solved numerically by using the fourth-order variable-step Runge-Kutta algorithm, and the bifurcation diagram of the interspike interval is plotted to study the evolution of the firing rhythm with the variation of parameters. It is found that the coupled system exhibits various typical bifurcation types, including inverse period-adding bifurcation, boundary crisis bifurcation, attractor merging crisis, and inverse period-doubling bifurcation, and the firing pattern changes from bursting to spiking. The effect of electrical coupling strength on the complete synchronization state of the coupled system is studied, and it is concluded that the electrical coupling strength is the dominant factor in determining whether the system enters the complete synchronization state; moreover, the larger the coupling strength is, the larger the parameter region occupied by the complete synchronization state becomes. The study of the bifurcation and synchronization states of the memristive neuron system can reveal the influence of different parameter values on the firing rhythm of the coupled system, and can also provide a theoretical reference for the treatment of biological neurological diseases.