Resumen de Phase Portraits of the Discontinuous Planar Piecewise Linear Differential Systems of Focus-Center Type

Li Xiong, Kuilin Wu, Shimin Li

• In this paper, we study the global phase portraits of the discontinuous planar piecewise linear differential system of the focus-center type and the center-center type with a straight line of separation. We obtain sufficient conditions for the existence and number of the crossing limit cycles and sliding limit cycles of the system. We prove the system of focus-center type and center-center type have 45 and 15 topologically different global phase portraits, respectively.