一类四维多项式系统非双曲奇点的稳定性与分岔

Stability of Nonhyperbolic Singular Point and Bifurcation in a Class of Four Dimensional Polynomial Systems

借助代数方法和Lyapunov函数,给出一类四维多项式中的三次微分方程的非双曲奇点的稳定性判据,研究具有球形中心的三次系统经过扰动后产生不变闭超曲面的分岔情况.

By using the algebra technics and Lyapunov function,this paper gives the condition for stability of nonhyperbolic singular point in a class of four dimensional polynomial systems with degree three.We also investigate the invariant closed hyper surface bifurcation when the three degree system with ballcenter is perturbed.