The study of periodic orbits in piecewise continuous differential systems

Abstract

In recent years, the study of piecewise dynamical systems has advanced rapidly. One of the problems investigated in this field is the calculation of limit cycles that bifurcate from the perturbation of a weak focus or of a periodic orbit. In this dissertation, we will present two methods used to compute the number of limit cycles that bifurcate from the perturbation of a system, namely Lyapunov constants method and the Melnikov function method.