时滞Rayleigh方程的稳定性与分支分析

Stability and Bifurcation Analysis for a Delayed Rayleigh Equation

对一类时滞Rayleigh方程的稳定性和Hopf分支进行了研究.首先,以滞量为参数,讨论了零解的稳定性及Hopf分支的存在性.然后,利用中心流形定理和规范型理论,给出了在第一个分支点处的分支方向及周期解的性质.

This paper deals with the delayed Rayleigh equation. Firstly, the stability of zero solution and the existence of Hopf bifurcation are discussed by analyzing the associated characteristic transcendental equation. Then, the direction and stability of bifurcating periodic solutions are determined by applying the center manifold theorem and normal form theory.