具有时滞的eHR神经元模型稳定性及Hopf分岔分析

Stability and Hopf Bifurcation Analysis of eHR Neuron Model with Time-Delay

摘要: 为研究时滞神经元系统复杂的动力学行为，本文在eHR神经元系统的基础上引入时滞项，通过分析线性化eHR模型系统在唯一平衡点的特征方程，得出某一临界值，使得超过其值时发生Hopf分岔，小于其值时，系统是渐进稳定的。此外，通过中心流形定理等理论给出了分岔周期解的稳定性和分岔方向。最后，为验证结论给出了部分数值模拟。

Abstract: In order to study the complex dynamic behavior of time-delayed neuron system, the time-delay term is introduced on the basis of eHR neuron system. By analyzing the characteristic equation of the linearized eHR model system at the unique equilibrium point, a critical value is obtained, so that Hopf bifurcation occurs when the value exceeds it, and the system is asymptotically stable when the value is less than it. In addition, the stability and bifurcation direction of the bifurcation periodic solution are given by the central manifold theorem and other theories. Finally, some nu-merical simulations are given to verify the conclusions.