FHN-ML神经元系统的稳定性及Hopf分岔研究

Study on Stability and Hopf Bifurcation of FHN-ML Neuron System

摘要: 基于电突触耦合神经元FHN-ML模型，讨论了该系统的平衡点及平衡点附近的稳定性，利用范式理论、Hassard等人降维方法，证明了系统Hopf分岔的存在并且确定了Hopf分岔的方向，给出了周期解与近似周期。最后，利用Matlab、C语言等数值模拟工具研究模型在单个参数下的分岔行为及动力学现象，验证了存在外界刺激对神经系统模型的干扰作用，应用最终的结论为神经元生理学实验提供理论依据。

Abstract: Based on the FHN-ML model of electro synaptic coupling neurons, the stability near the equilibrium point and the equilibrium point of the system are discussed. The existence of Hopf bifurcation and the direction of Hopf bifurcation are proved by using the normal form theory and Hassard method. The periodic solution and approximate period are given. Finally, this paper uses numerical simulation tools such as MATLAB, C language to study the bifurcation behavior and dynamics of the model under a single parameter, verify the interference of external stimuli on the neural system model, and apply the final conclusion to provide a theoretical basis for neuron physiological experiments.