一类三次微分系统的异宿环分支 Bifurcations of Heteroclinic Loop for a Class of Cubic Differential Systems

本文运用分支的方法，通过分析未扰系统的异宿环在小扰动下的稳定流形和不稳定流形之间的相对距离，研究了一类三次微分系统的异宿环分支极限环的问题，给出了系统至少产生一个极限环的条件。 In this paper, by using the bifurcation method to analyze the relative distance between the stable manifold and the unstable manifold after the heteroclinic loop of the unperturbed system was perturbed to break, the authors studied the existence problem of limit cycles of a class of cubic differential system and obtained the conditions to ensure the system has at least one limit cycle.