一类含时滞非线性微分方程组的Hopf分歧

Hopf Bifurcation for a Class of Nonlinear Differential Equation System with Delays

本文应用Hopf分歧定理,讨论一类含时滞非线性微分方程组的Hopf分歧问题。分析了这类方程组零解的稳定性以及产生Hopf分歧的条件,得到了它的分歧周期解的存在性、稳定性以及它的渐近形式。

By using the theoem of Hopf bifurcation, this paper discusses the problem of Hopf bifurcation for a class of the nonlinear differential equation system with delays. The existence and stability of bifucating periodic solutions for this class of the equation system is proved. The asymptotic form and periods of the small amplitude periodic solutions bifurcating from the steady state are obtained.