Time and resonance patterns in chaotic piece-wise linear systems

Abstract

The aim of this paper is to characterize time and resonant behavior in a class of piece-wise linear systems evolving chaotically. To this end, statistical methods are used to reveal interactions of different parts of the system. The system under study comprises a continuous time subsystem and a switching rule that induces an oscillatory path by switching alternately between stable and unstable conditions. Since the system is not continuous, the principal oscillation frequency depends on the switching regime and linear subsystem parameters; therefore, many time and resonant patterns can be observed. It is shown that the system may display resonance produced by the action of a external signal (switching law), as well as internal and combinational resonance. The effect of system parameters on time evolution and resonance is studied. It is shown that the nature of subsystems eigenvalues plays a crucial role in the type of resonance observed, producing in some cases complex interaction of resonance modes.