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 ,研究了二次微分系统(Ⅲ )类方程 x =-y +δx +mxy +y2 , y =x(1+ax +by)的同宿轨分支极限环的问题 .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 unperturbed system under small perturbation,the problems of limit cycles bifurcated from the homoclinic orbit for the type (Ⅲ) equation =-y+δx+mxy-y 2,=x(1+ax+by) of quadratic differential systems was studied.The conditions were given to ensure the system has stable limit cycle and unstable limit cycle,respectively.
基金
国家自然科学基金资助课题 [10 0 710 2 2 ]
