一类平面二次系统(Ⅲ)类方程的同宿分支问题  

The Homoclinic Bifurcation Problems of a Class of Type (Ⅲ) Equations of Planer Quadratic Systems

作　　者：王宁宁[1,2] 祝晓薇[1] 张利群[1] 丁本艳[1] 

机构地区：[1]临沂大学理学院,山东临沂276005 [2]山东师范大学数学科学学院,山东济南250014

出　　处：《枣庄学院学报》2013年第2期23-27,共5页Journal of Zaozhuang University

摘　　要：通过分析未扰系统的同宿轨在小扰动下的稳定流形和不稳定流形之间的相对位置,研究了一类二次微分方程的同宿轨分支极限环的存在性问题,给出了系统存在唯一稳定或者不稳定极限环的条件.By analyzing the relative position of the stable manifold and the unstable manifold of the homoclinic orbit for the unperturbated system under small perturbation, the author studied the existence problems of limit cycles bifurcated from the homoclinic orbit for a class of equations of quadratic differential systems. The conditions were given to ensure the system has stable limit cycle and unstable limit cycle, respectively.

关 键 词：同宿轨 分支 P—B环域定理 极限环 

分 类 号：O177.91[理学—数学]