Study of limit cycles in piecewise smooth perturbations of Hamiltonian centers via regularization method

Abstract

In this article we study the existence and positions of limit cycles in piecewise smooth perturbations of planar Hamiltonian centers. By using the regularization method we provide an analytical expression for the first order Melnikov function frequently used in the literature directly from the original non-smooth problem.

Keywords

• piecewise smooth system
• limit cycle
• periodic orbit
• regularization method
• melnikov function