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Volume 8, Number 5, 2018, Pages 1441-1451                                                                DOI:10.11948/2018.1441
Bifurcation of limit cycles from the global center of a class of integrable non-Hamilton systems
Shiyou Sui and Baoyi Li
Keywords:Limit cycle, averaging function, bifurcation.
Abstract:
      In this paper, we consider the bifurcation of limit cycles for system $\dot{x}=-y(x^2+a^2)^m,~\dot{y}=x(x^2+a^2)^m$ under perturbations of polynomials with degree n, where $a\neq0$, $m\in \mathbb{N}$. By using the averaging method of first order, we bound the number of limit cycles that can bifurcate from periodic orbits of the center of the unperturbed system. Particularly, if $m=2, n=5$, the sharp bound is 5.
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