具时滞神经反馈模型的动力学性质

Dynamics of neural feedback model with time delay

以滞量τ为分支参数,研究了具有时滞项的神经反馈模型的动力学行为,这些行为包括:系统在平衡点附近的稳定性、局部Hopf分支的存在性、发生条件、Hopf分支的方向、分支周期解的稳定性以及分支随参数变化其周期解的周期变化.最后通过数值模拟验证了理论分析结果,给出了Hopf分支全局存在性的数值结果.

We study the dynamic behaviors of delay Neural feedback Model with the time delay,using delay r as bifurcation parameter. These behaviors include the stability near the equilibrium point, the existence of the local Hopf bifurcation, the condition of occurrence, the direction of the Hopf bifurcation, the stability of the periodic solution, and the cycle of the periodic solution of the bifurcation changing with the parameter change. Finally, numerical simulations are carried out to support the theoretical findings,and also show a numerical result about the existence of global Hopf bifurcation.