一类n次微分系统的全局分支  

Global bifurcations of a kind of n-dimensional differential system

作　　者：胡召平[1] 

机构地区：[1]上海交通大学数学系,上海200240

出　　处：《上海师范大学学报（自然科学版）》2008年第4期362-368,共7页Journal of Shanghai Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(10671127)

摘　　要：利用已有的关于Lienard系统极限环存在性和唯一、唯二性的诸多结论,结合旋转向量场理论,研究了n次微分系统x.=y,y.=-(hxn-1+δ)y-(xn-x)(h>0)当n为大于1的正整数时极限环的个数及其相互位置,并利用先前的结果作为特例,得到了相当完善的结果.By virtue of some known results of the existence on at most one or two limit cycles of the Lienard systems, using the theory of rotated vector field, we study the number and relative positions of the limit cycles of the n - demensional differential system x=y,y=-（hx^n-1＋δ）y-（x^n-x）（h〉0）, where n is a positive integer greater than 1 . We obtain rather perfect results, which include many results that have been gained by former scholars as special cases.

关 键 词：LIENARD系统 极限环 旋转向量场 

分 类 号：O175.12[理学—数学]