达布多项式和二次系统周期解的存在性  

Existence of Darboux polynomial and periodic orbit of a quadratic system

作　　者：邓桂丰[1] 

机构地区：[1]上海立信会计学院数学与信息学院,上海201620

出　　处：《华东师范大学学报（自然科学版）》2010年第5期84-90,共7页Journal of East China Normal University(Natural Science)

基　　金：上海市高校选拔培养优秀青年教师科研专项基金(slx08018);上海市本级财政部门预算项目(1130IA15;1139IA0013)

摘　　要：给出了平面高次系统具有不变实不可约达布多项式的充要条件.在此基础上利用代数方法,根据平面二次系统表达式中的二次多项式来判定系统平衡点是否有闭轨线环绕,进而指出闭轨线内部的平衡点必须具备的一些条件.This paper derived the necessary and sufficient condition for the existence of invariant real irreducible algebraic curve of a polynomial differential system. Using this result and quadratic polynomials of quadratic system, we established some criteria to determine whether equilibrium was circled by a closed orbit. Finally, a property of the equilibrium enclosed in a periodic orbit was deduced for quadratic system.

关 键 词：不可约达布多项式 不变代数曲线 平面二次系统 周期解 

分 类 号：O175.2[理学—数学]