电磁激励下具有混合突触耦合的Chay神经元系统动力学特性研究

Research on the Dynamical Characteristics of Chay Neuron Systems with Hybrid Synaptic Coupling under Electromagnetic Excitation

摘要: 为了研究混合突触对神经元放电模式和同步状态的影响，考虑电磁激励下Chay神经元模型，采用变步长四阶Runge-Kutta算法进行数值计算。利用峰峰间期分岔图、相图、时间历程图以及双参数分岔图研究不同参数对耦合系统分岔的影响，得出耦合神经元系统在不同的参数值下可产生周期放电、逆倍周期放电和混沌簇放电。利用相似函数同步统计量，研究耦合神经系统同步行为，得出增大耦合强度可促进耦合系统的同步行为，可揭示耦合系统神经信息的编码和传递机制，为治疗神经性疾病提供理论基础。

Abstract: To investigate the effects of mixed synaptic on neuronal firing patterns and synchrony states, the Chay neuronal model under electromagnetic excitation is considered, and numerical calculations are performed using a variable-step fourth-order Runge-Kutta algorithm. Using peak-to-peak bifurcation diagrams, phase diagrams, time-history plots, and two-parameter bifurcation diagrams, the effects of different parameters on bifurcation in coupled systems are investigated. It was found that coupled neural systems can generate periodic discharges, inverse-periodic discharges, and chaotic cluster discharges under different parameter values. Synchronizing statistics using similarity functions, the synchronization behavior of coupled neural systems is investigated, and it is concluded that increasing coupling strength promotes synchronization in coupled systems. This reveals the encoding and transmission mechanisms of neural information in coupled systems, providing a theoretical foundation for treating neurological disorders.