Global phase portraits of planar piecewise linear refracting systems of saddle–saddle type

Abstract

This paper deal with the global dynamics of planar piecewise linear refracting systems of saddle–saddle type with a straight line of separation. We investigate the singularities, limit cycles, homoclinic orbits, heteroclinic orbits and make the classification of global phase portraits in the Poincaré disk for the refracting systems. We prove that these systems have 18 topologically different global phase portraits.