具有任意激活函数的时延神经元方程的Hopf分岔

该文研究了一个带时延的神经元方程,分析相应的线性化方程的超越特征方程,研究了这个模型的线性稳定性,对于神经元来自过去状态的抑制影响,作者发现当这个影响值变化并通过一个临界序列时,这个模型会出现Hopf分岔,利用规范形式理论和中心流形定理,解析确定了周期解的稳定性与Hopf分岔方向,数值例子也证实了所得结论。

Hopf bifurcation for delayed neuron equation with arbitrary activation function

In this paper, a neural equation with discrete time delay is studied, The transcendental equation corresponding to the above-mentioned linearized system is analyzed. The linear stability for this model has been investigated. For the case with inhibitory influence from the past state, it is found that Hopf bifurcation occurs when this influence varies and passes through a sequence of critical values. The stability of bifurcating periodic solutions and the direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Some numerical examples illustrated those results.