On the crossing periodic orbits of a piecewise linear Lienard-like system with symmetric admissible foci

Abstract:

We investigate the crossing periodic orbits of a piecewise linear Lienard-like system with symmetric admissible foci. By reducing the system to a normal form with less parameters and constructing the Poincare maps for the left and right subsystems, we show the existence of at least one crossing periodic orbit, give a sufficient condition for the non-existence of crossing periodic orbits, and provide an upper bound for the number of crossing periodic orbits under some conditions.