Crossing limit cycles of a 3D piecewise-smooth system

Abstract:

In this paper we investigate the crossing limit cycles of a 3D discontinuous piecewise-smooth system. In this system, the phase space is divided into two regions by a hypersurface and thus the system presents two different vector fields. Meanwhile, the system presents two-fold in which both vector fields are tangent to the hypersurface. We prove that the maximum number of crossing limit cycles is 2 and give necessary and sufficient conditions for one and two crossing limit cycles respectively. Furthermore, the crossing locations of crossing limit cycles are all determined as well as their periods.