DETECTION FUNCTION METHOD AND ITS APPLICATION TO A PERTURBED HAMILTONIAN SYSTEM

Abstract

A Hamiltonian system with 25 singular points under five-order perturbed terms is introduced in this paper in order to study the existence, number and distribution of limit cycles. The detection function method is employed. First we classify the type of the closed curves of the unperturbed system, then we obtain the analytical forms of the detection functions of the perturbed system. Finally, by numerical explorations, we point out the distribution of the limit cycles for a particular case.