On Motions of a Dynamical System with a Relay Hysteresis

We study an $n$-dimensional system of ordinary differential equations (ODEs) with a relay nonsymmetric hysteresis. Conditions under which the system of ODEs governs a dynamical system are specified. We obtain sufficient conditions for motions of the system to be recurrent or periodic. Also, we consider various configurations for the closed phase trajectories (orbits) of the motions as well as properties of fixed (switching) points on these trajectories. An example for the system of dimension 3 is given to support the obtained results.