Using Melnikov functions of any order for studying limit cycles (Q2374237)

The planar system investigated in the paper is related to Hilbert's 16th problem. The author studies a class of quadratic Hamiltonian systems perturbed with general quadratic polynomials in order to identify the maximum number of limit cycles. He derived the Melnikov functions arisen from the displacement function of the first return map. By choosing appropriate system parametric values and taking into account the Melnikov functions of any order, the author shows that the planar system has at most three limit cycles which bifurcate from the period annulus of the unperturbed system and this upper bound is reached.