电磁场下HR神经元模型分岔分析

Bifurcation analysis of HR neuron model in electromagnetic field

电磁场对神经元的放电活动有着重要影响,但是目前还无法精确给出电磁场对神经元放电活动影响的具体关系式。本文运用理论与仿真相结合的方法,分析了在外界刺激电流的变化下系统平衡点的分布与稳定性,理论分析得出该系统存在超(亚)临界Hopf分岔行为,并在亚临界Hopf分岔点附近发现了隐藏吸引子。基于理论分析,数值仿真该系统在Hopf分岔点附近的放电特征,揭示了电磁场下HR神经元模型放电特征转变的内在机制。

Electromagnetic field has an important influence on the discharge activity of neurons,but at present,it is impossible to give the specific relationship of the influence of electromagnetic field on the discharge activity of neurons.In this paper,the distribution and stability of the equilibrium point of the system under the change of external stimulation current are analyzed by using the method of theory and simulation.It is concluded that there is a super(subcritical)Hopf bifurcation behavior in the system,and a hidden attractor is found near the subcritical Hopf bifurcation point.Based on the theoretical analysis and numerical simulation of the discharge characteristics of the system near the Hopf bifurcation point,the internal mechanism of the discharge characteristic transformation of HR neuron model under electromagnetic field is revealed.