The cyclicity of period annuli of a quadratic reversible Lotka-Volterra system with two centers

Abstract

This paper is concerned with the bifurcations of limit cycles in a quadratic reversible Lotka-Volterra system with two centers under quadratic perturbations. By studying the number of zeros of Abelian integral based on the geometric properties of some planar curves, we obtain the cyclicity of each periodic annulus of the system under quadratic perturbations is two, and the cyclicity of two period annuli is three. In addition, we present the configurations of limit cycles of the perturbed system. Mathematics Subject Classification: 34C07, 34C08, 37G15