Quadratic perturbations of a class of quadratic reversible systems with two centers (Q1030533)

The paper is devoted to quadratic perturbations of a one parameter family of quadratic reversible non-Hamiltonian systems \[ \dot{x}= -y - 0.5x^2 + (k+1)y^2, \;\dot{y}= x (1-2y) \] with two non-degenerate centers (\(|k|<1\)) and without other singularities in the finite plane. By using the investigation of zeros of an Abelian integral the exact upper bound for the number of limit cycles that emerge from each of the two period annuli is given. The configurations of limit cycles and the corresponding bifurcation diagrams for different range of the parameter are presented.