Quadratic perturbations of a quadratic reversible Lotka-Volterra system

Abstract

We prove that perturbing the two periodic annuli of the quadratic polynomial reversible Lotka-Volterra differential system ̇x = -y + x2 - y2, ẏ = x(1 + 2y), inside the class of all quadratic polynomial differential systems we can obtain the following configurations of limit cycles (0,0), (1,0), (2,0), (1,1) and (1,2).