二维三次多项式系统的奇点与异宿环分支分析  

The Analysis of Singularities and Bifurcation of Heteroclinic Loops of Two-Dimensional Cubic Polynomial Systems

作　　者：姜文雅 潘桂荣 丁文静 李佳 李夏 

机构地区：[1]临沂大学数学与统计学院,山东临沂 [2]临沂大学信息科学与工程学院,山东临沂

出　　处：《理论数学》2019年第5期578-584,共7页Pure Mathematics

基　　金：山东省自然科学基金(ZR2018MA016,ZR2015AL005);山东省软科学研究计划项目(2012RKA13021);临沂大学大学生创新创业训练计划项目(201710452001)。

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。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.

关 键 词：三次多项式系统 奇点 异宿环 分支 极限环 

分 类 号：O1[理学—数学]