带多个时间滞量的泛函微分方程的Hopf分支的定向、周期估计和稳定性的实用公式判据

Orientation, Periodic Estimation and Stability of Funtional Differential Equation of Hopf Bifurcation with Several Delays

本文利用中心流形定理和规范形方法来研究带有n个时间滞量的泛函微分方程 x=F(μ,x(t-r_1),x(t-r_2),…,x(t-r_a)),其中μ∈R,x∈C=C([-r,0],R^n),r_i>0,F(μ,φ(r_1),φ(r_2),…,φ(r_a))连续,对μ和φ有连续的一阶导数,对所有的μ有F(μ,0,0,…,0)=0的Hopf分支的定向、周期估计和稳定性等动力系统性态,得到了强有力的实用公式判据。

In this paper, using the Center Manifold Theorem and Norm Form Theory, we derive the fomula of Orientation, Periodic Estimation and Stability of Hopf Bifurcation of Functional Differential Equation with several delays x=F(μ, x(t—γ_1,x(t—γ_2), …, x(t—γ_n)), μ∈R, x∈C, γ_i>0.