对一类具有时滞的神经反馈模型,利用超越函数的零点分布定理和规范型理论,研究系统平衡点的稳定性和局部Hopf分支的存在性,得到了确定分支方向及分支周期解稳定性的计算公式,并给出了Hopf分支全局存在性的数值结果.数值模拟实验验证了理论结果.
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.