一类环面上微分系统极限环的唯n性  

Existence of Exact n Limit Cycles for Differential Systems on Torus

作　　者：郭瑞海[1] 

机构地区：[1]西南民族学院计科系,成都610041

出　　处：《西南民族学院学报（自然科学版）》2001年第2期140-144,共5页Journal of Southwest Nationalities College(Natural Science Edition)

摘　　要：利用含参数微分方程的周期解与极限环的理论 ,证明了环面T2 :C1×C2 (C1:-π <x≤π ,C2 :-π <y≤π)上的微分系统 x =siny , y =-sinx +μsin3y围绕奇点 0 ( 0 ,0 )有且仅有By the general theory on periodic solutions and limit cycles of differential equations with one parameter,the problems on the limit cycles for the differential systems on the torus are studied. The important results of the exact number of the limit cycles are obtained:there are exact two limit cycles of the first kind around the singular point O (0.0) for the given system.

关 键 词：环面 微分系统 极限环 椭圆积分 

分 类 号：O175[理学—数学] O153.3[理学—基础数学]