具有平行直线解的三次系统的中心焦点判定与极限环的唯一性  

Determination of center focus and uniqueness of limit cycle for a class of cubic system

作　　者：谢向东[1] 占青义[2] 

机构地区：[1]宁德师范高等专科学校,福建宁德352100 [2]福建农林大学计算机与信息学院,福建福州350002

出　　处：《福州大学学报（自然科学版）》2010年第3期336-341,共6页Journal of Fuzhou University(Natural Science Edition)

基　　金：福建省自然科学基金资助项目(2010J0201;2008J0185)

摘　　要：研究一类具有平行直线解的三次系统的中心焦点判定和极限环的存在唯一性.采用Lienard方程计算焦点量,用数形结合和定性与定量结合的分析方法证明极限环的唯一性.研究结果表明:该三次系统可以存在2个极限环,在细焦点外围至多有一个极限环,在二阶细焦点外围无极限环.This paper studied the determination of center focus,existence and uniqueness of limit cycle for a class of cubic system which has parallel line solution.Lienard function is used in focus calculation,the method of combination of mathematics and figure,quantitative and qualitative analysis are all used in the proof of uniqueness of limit cycle.It shows that system（4）have two limit cycles surrounding O（0,0）,no more than one limit cycle surrounding weak focus O and no limit cycles surrounding weak focus O of degree 2.

关 键 词：三次系统 中心焦点 判定 极限环 唯一性 

分 类 号：O175.12[理学—数学]