摘要
通过分析未扰系统的同宿轨在小扰动下产生的稳定和不稳定流形之间的相对位置,利用环域定理,研究了一类平面二次系统(Ⅱ)类微分方程的极限环的存在性问题,给出了系统存在唯一稳定及不稳定极限环的条件.
In this paper, by analyzing the relative position of the stable manifold and the unstable manifold for the homoclinic orbit of the unperturbated system under small perturbation, and using annular region theorem, the author studies the existence problem of limit cycles bifurcated from the homoclinic orbit for the type （II） differential equation of planar quadratic systems. The conditions are given to ensure the system has unique stable limit cycle and unique unstable limit cycle respectively.
出处
《临沂大学学报》
2013年第3期95-99,共5页
Journal of Linyi University
基金
国家自然科学基金资助课题(10671069)
山东省自然科学基金资助课题(Y2007A17)
关键词
同宿轨
流形
P-B环域定理
分支
极限环
homoclinie orbit
manifold
annular region theorem
bifurcation
limit cycle
