一多项式系统的极限环

Limit Cycle for a Polynomial System

讨论了系统 ｄｘｄｔ＝ － ｙ（１＋ ｙ）α＋ ｄ·ｘα＋ ｘα＋ １＋ ｄｘαｙｄｙｄｔ＝ ｘα（１＋ ａｘ＋ ｙ）的极限环．彻底解决了该系统极限环存在的个数和分布问题．讨论的结果包含了文［１］的所有结果，并且一些结果好于文［１］．（α为正的奇数）．

In this paper,the limit cycle of following polynomial system was discussed \%d\%x\%d\%t=-y(1+y) α+dx α+x α+1 +dx αy \%d\%y\%d\%t=x α(1+ax+y) where α is a positive odd number.We completely solved the problem of numbers and position of limit cycles for the system.All results of article [1] was contained in this paper,and some of our results are better than those in article[1].