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,研究了平面二次微分系统具有如下形式的(Ⅲ)类方程.=-y+δx+mxy+ny2,.=x(1+ax+by)(b≠0,n≠0)的同宿分支极限环的问题.给出了系统分别存在稳定极限环和不稳定极限环的条件.
By analyzing the relative position of the stable manifold and the unstable manifold for the unperturbated system under small perturbation, the author studied the problems of limit cycles bifurcated from the homoclinic orbit for the type （Ⅲ） equation x=-y＋δx＋mxy＋ny^2,y=x（1＋ax＋by）（b≠0,n≠0）of quadratic differential systems. The conditions were given to ensurethat the system has stable limit cycle and unstable limit cycle, respectively.
出处
《齐鲁师范学院学报》
2012年第2期98-102,共5页
Journal of Qilu Normal University
基金
国家自然科学基金(10671069)
山东省自然科学基金(Y2007A17)资助课题
关键词
同宿轨
流形
P—B环域定理
分支
极限环
Homoclinic orbit
Manifold
P - B annular region theorem
Bifurcation
Limit cycle.
