Bifurcation of limit cycles at infinity in a class of switching systems

Abstract

In this paper, we present a method to compute focal values and periodic constants at infinity of a class of switching systems and apply it to study a cubic system. We prove that such a cubic system can have 7 limit cycles in the sufficiently small neighborhood of infinity. Moreover, we consider a quintic switching system to obtain 14 limit cycles at infinity, while continuous quintic systems can have only 11 limit cycles in the sufficiently small neighborhood of infinity. This indicates that switching systems or discontinuous systems can exhibit more complex dynamics compared to smooth systems.