关于Hopf分歧定理的一个讨论

关于 Hopf分歧定理已有许多人进行了细致的研究并作了推广 ,作者利用常微分方程定性理论对于高阶奇点的 Hopf分歧产生的条件 ,出现的分歧集合及其扰动出来的闭轨线的个数进行了分析探讨 ,得到了一个更为广泛的结果 :当孤立奇点的渐近稳定性发生改变时 ,奇点将分歧出极限环或奇异闭轨 ,并举例说明了高阶奇点附近轨线分布的复杂性

A Discussion about the Hopf Bifurcation Theorem

There are many papers to study and generalize the Hopf bifurcation theorem. In this paper, we analyze the condition, the bifurcated set and the number of closed orbits of Hopf bifurcation about the higher order critical point by quality theory of differential equations. We get a more general conclusion: when the asymptotic stability of a isolated critical point is changing, limit cycles or polycycles would be bifurcated out. We show the complexity of orbits in the neighborhood of the higher order critical point by an example in the end.