Dynamics of a Switched by Hysteresis Linear System in R2

This paper examines the local and global behavior of a two-variable piece-wise smooth dynamic system by studying the flow of two nonhomogeneous linear dynamic systems that switch on the boundaries of a hysteresis band. Both equilibrium solutions and parametric domains that guarantee the existence of periodic orbits within the band, were determined analytically. While, phase portraits and basins of attraction of the system for different values of the parameters were performed through numerical simulations. Results show the coexistence of multiple stationary states of different types when different parameter values are used