关于一类扰动系统的极限环上界问题

About a problem of upper bound of limit cycles of a class perturbed system

本文讨论了一类扰动系统在其一阶 Melnikov函数恒为零 ,而二阶 Melnikov函数不恒为零时的 Poincare分支及 Hopf分支的有关问题 ,得到了该系统的极限环个数的上界估计 .本文推广并深化了文 [4]的结论 ,也弥补了该文的某些不足 .

In this paper, about the problem of Poincare bifurcation and Hopf bifurcation for a class perturbed system are discussed, we get an estimate of the upper bound of the number of limit cycles when M 1(h)≡0 and M 2(h)0, this paper extend and deepen the conclusion of [4] and also fetch up some lack of [4].