摘要:
本文研究了三次微分系统
的异宿环分支极限环问题。作者利用Melnikov函数计算未扰系统的异宿轨经扰动破裂以后的稳定流形和不稳定流形之间的相对距离，结合奇点的类型与稳定性分析，给出了系统存在稳定极限环和不稳定极限环的条件。
Abstract:
In this paper, the authors studied the problem of limit cycle bifurcated from heteroclinic loop for the cubic polynomial system
Assume that the heteroclinic orbit of the undisturbed system is broken after being disturbed. By analyzing the relative distances between the stable manifolds and the unstable manifolds of the disturbed system under small perturbations, combining the analysis of the types and stability of singularities, the authors obtained the conditions for the existence of stable and unstable limit cycle for the system.