Bifurcation Analysis of a Planar Piecewise Linear System of Focus–Focus Type

Abstract

This paper is devoted to discussing the sliding bifurcation phenomena of a planar piecewise linear system with two zones separated by a straight line. We consider those systems for which in each zone there is precisely one real focus. By introducing Poincaré map and defining proper displacement function, some results on the existence of crossing periodic orbits, sliding periodic orbits, sliding-crossing periodic orbits and sliding homoclinic connections are obtained. Moreover, we establish some conditions for the simultaneous occurrence of crossing and sliding periodic orbits and show a concrete example.