二次微分系统(Ⅱ)类方程的分支问题  

THE BIFURCATION PROBLEMS OF TYPE (Ⅱ) EQUATION OF QUADRATIC DIFFERENTIAL SYSTEMS

作　　者：郑庆玉[1] 

机构地区：[1]临沂师范学院数学系,山东省临沂市276005

出　　处：《曲阜师范大学学报（自然科学版）》2002年第3期27-30,共4页Journal of Qufu Normal University(Natural Science)

摘　　要：研究二次微分系统 (Ⅱ )类方程 x =- y +δx +mxy - y2 , y =x(1+ax)的极限环的存在性问题 .运用分支方法 ,分析了未扰系统的同宿轨破裂以后稳定流形和不稳定流形之间的距离 .The author considered the existence problem of limit cycles of the type (Ⅱ) equation =-y+δx+mxy-y 2, =x(1+ax) of quadratic differential systems. The bifurcation method was used to analyze the distance between the stable manifold and the unstable manifold after the homoclinic orbit of the unperturbed system was perturbed to break. The conditions were given to ensure the generation of at least one and two limit cycles.

关 键 词：二次微分系统 (Ⅱ)类方程 分支问题 同宿轨 分支方法 极限环 存在性 轨线结构 

分 类 号：O177.91[理学—数学] O175.12[理学—基础数学]