三次系统极限环的分支研究

摘要

从微分方程一般理论出发,研究了平面三次多项式系统在原点周围和赤道附近同时产生极限环分支的情形.通过改变位于原点的奇点的稳定性,结合分析三次系统向量场在无穷远处的分支,得到了恰有一个无穷远奇点的三次系统分别在原点周围和赤道附近同时存在多个极限环的充分条件.%Start with the general theory and then specialized to the particular case of cubic polynomial systems for which the simultaneous bifurcation of limit cycles from the origin and the equator is studied.By means of method of changing the stability of singular at the origin,combining with the method of researching the bifurcation at infinity in vector fields of cubic system,the sufficient conditions for the existence of several limit cycles around the origin or near the equator respectively to a class of cubic system which has exactly an unique singular point at infinity are obtained.