一类三次系统的中心焦点判定与极限环的唯一性  

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

作　　者：谢向东[1] 陈凤德[2] 

机构地区：[1]宁德师范高等专科学校,福建宁德352100 [2]福州大学数学与计算机学院,福建福州350002

出　　处：《宝鸡文理学院学报（自然科学版）》2007年第4期249-253,共5页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金(数学天元基金)(104260106);福建省自然科学基金资助项目(Z0511052)

摘　　要：目的研究一类三次系统的中心焦点判定和极限环的存在唯一性。方法采用Lienard方程的方法计算焦点量,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。结果推广了部分参考文献所研究的方程类型和已有的结论。结论表明该三次系统.x=-y+δx+lx2+mxy+ny2,.y=x(1+ay-y2)可以存在2个极限环,该系统在细焦点外围至多有一个极限环。Aim To study the decision of center and focus,and the uniqueness of limit cycle for a class of cubic system. Methods The both qualitation analysis and quanlititative analysis were used in proof of uniqueness of limit cycle. Results Extending the equation and conclusions which had studied. Conclusion The results showed that the system, x^·=-y＋δx＋lx^2＋mxy＋ny^2,y^·=x（1＋ay-y^2）, exist two limit cycles and has at most one limit cycle surrounding weak focus.

关 键 词：相伴系统 三次系统 极限环的唯一性 细焦点 

分 类 号：O175.12[理学—数学]