双曲线边界二次系统单中心环域的Poincaré分支  

Poincaré bifurcation for quadratic system with a bound of hyperbola and a single center

作　　者：谭欣欣[1] 冯恩民[1] 沈伯骞[2] 

机构地区：[1]大连理工大学应用数学系 [2]辽宁师范大学数学系,辽宁大连116029

出　　处：《大连理工大学学报》2005年第2期298-302,共5页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(10471014);大连大学科技发展基金资助项目.

摘　　要：对一类以双曲线为边界的二次系统单中心环域的Poincaré分支问题,首次采用将Abel积分进行幂级数展开的方法,借助于Matlab编程计算,证明了在它的中心环域内可以分支出位置具有任意性的2个极限环.这种方法简便易行,更适用于高次多项式系统.Aiming at the problem of Poincaré bifurcation for the quadratic system with a bound of hyperbola and a single center, the method of the power series expansion for Abelian integral by Matlab program is proposed for the first time. It is proved that there are at least two limit cycles produced from its center region. Moreover, these two limit cycles are with arbitrary location. The method is feasible, it is more suitable for higher order polynomial systems.

关 键 词：POINCARE分支 二次系统 环域 曲线边界 Abel积分 Matlab 幂级数展开 多项式系统 分支问题 编程计算 双曲线 极限环 任意性 

分 类 号：O175.12[理学—数学] O175.25[理学—基础数学]