Perturbations of May-Leonard System

Zhao Yulin; Cen Xiuli

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Perturbations of May-Leonard System

Zhao Yulin *,Cen Xiuli

Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P.R.China

*Correspondence author

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Funding: none

Opened online: 7 March 2014

Accepted by: none

Citation: Zhao Yulin,Cen Xiuli.Perturbations of May-Leonard System[OL]. [ 7 March 2014] http://en.paper.edu.cn/en_releasepaper/content/4588219

In this paper we study the quadratic perturbations of the 3-dimensional May-Leonard system with $lpha+eta=2$. It is shown that there are perturbed systems having exactly one or two limit cycles bifurcating from the periodic orbits of May-Leonard system eqref{ML}. This is proved by estimating the number of zeros of the first and the second order Melnikov functions.

Keywords:3-dimensional Limit cycles; May-Leonard systems; Hamiltonian systems; Melnikov functions; Chebyshev systems.

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