Bifurcations of limit cycles from quadratic non-Hamiltonian systems with two centres and two unbounded heteroclinic loops

Abstract

We investigate the bifurcations of limit cycles in a class of planar quadratic integrable (non-Hamiltonian) systems with two centres, both surrounded by unbounded heteroclinic loops, under small quadratic perturbations. By a careful study of the number of zeros of Abelian integrals based on the geometric properties of some planar curves, defined by ratios of such integrals, we obtain complete results about the number and the distribution of limit cycles bifurcating from the two period annuli.