关键词: 神经反馈模型, 时滞, 稳定性, 局部Hopf分支, 全局Hopf分支

Abstract:

On the basis of the zero distribution theorem of transcendental function and normal form theorem, the authors studied the stability and local Hopf bifurcation of a neural feedback model with time delay. Further, the authors  also obtained the formulas, which decide the direction of Hopf bifurcation, and the stability of the period solution. Finally, numerical simulations were carried out to support the theoretical findings, and  a numerical result about the existence of global Hopf bifurcation was given.

Key words:  neural feedback model, time delay, stability, local Hopf bifurcation, global Hopf bifurcation