一类n次微分系统的全局分支

Global bifurcations of a kind of n-dimensional differential system

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.