二次系统二阶细焦点外围极限环的唯一性  

On the Uniqueness of the Limit Cycle of the Quadratic System with a 2nd-Order Weak Focus

作　　者：张平光[1] 

机构地区：[1]浙江大学数学系,杭州310027

出　　处：《数学学报（中文版）》1999年第2期289-304,共16页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金

摘　　要：本文证明了平面二次系统二阶细焦点外围至多存在一个极限环这一猜想，并证明了若第二、第三焦点量的乘积大于零，则在二阶细焦点外围不存在极限环．In this paper,we prove that the plane quadratic system has at most one limitcycle surrounding a 2nd-order weak focus, and that if the product of the second andthird focus value of the weak focus is positive definite, then the system has no limitcycle surrounding the 2nd-order weak focus.

关 键 词：二次系统 二阶细焦点 极限环 唯一性 微分系统 

分 类 号：O175.12[理学—数学]