一类具退化奇点的五次系统中心条件及极限环分支  

Bifurcations of Limit Cycles Created from a Three-order Nilpotent Critical Point of a Quintic System

作　　者：李锋[1] 金银来[1] 何西兵[2] 

机构地区：[1]临沂大学理学院,临沂276005 [2]西安交通大学数学与统计学院,西安710049

出　　处：《工程数学学报》2012年第2期262-266,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10771196);山东省自然科学基金(2007A17)~~

摘　　要：本文研究了一类原点为幂零奇点的五次微分系统,通过计算系统的前7个Lyapunov常数,得到了系统的原点为中心的充要条件,并证明了系统在原点至多能够分支出5个极限环.同时研究了系统其余四个奇点(±1,0),(0,±1)的中心焦点问题,分别得到了系统存在5个中心、3个中心的条件.In this paper,a class of quinic polynomial differential system with nilpotent critical point are investigated.The first 7 quasi Lyapunov constants are deduced with the help of computer algebra system mathematica.As a result,the sufficient and necessary conditions of the center in the system are derived.There exist 5 small amplitude limit cycles created from the three order nilpotent critical point is also proved.Others critical points（±1,0）,（0,±1） are researched at the same condition,the sufficient and necessary conditions of existing five or three centers in the system are obtained respectively.

关 键 词：幂零奇点 中心 焦点 极限环分支 

分 类 号：O175.12[理学—数学]