Quadratic perturbations of a quadratic reversible Lotka-Volterra system with two centers

This paper is concerned with the bifurcation of limit cycles from aquadratic reversible Lotka-Volterra system with two centers of genusone under small quadratic perturbations. It shows that thecyclicities of each period annulus and two period annuli of theconsidered system under small quadratic perturbations are two,respectively. This not only gives at least partially a positive answer toan open conjecture, but also improves the corresponding results in the literature.In addition, we present the configurations oflimit cycles of the perturbed system as (2, 0), (1, 1), (1, 0),(0, 2), (0, 1) and (0, 0), where $(i,\, j)$ indicates that theperturbed system has $i$ limit cycles surrounding the positivesingularity while it has $j$ limit cycles surrounding the negative one.