Existence and destruction of tori in a discontinuous oscillator under quasi-periodic excitations

Abstract

We investigate the existence and destruction of invariant tori in a discontinuous oscillator under quasi-periodic excitation. For the conservative case, by constructing a quasi-periodic twist map, we prove the existence of infinitely many invariant tori and show that all solutions of the system are bounded when the frequencies satisfy the non-resonance condition. For the dissipative case, by taking a quasi-periodic forcing with two frequencies, we employ numerical methods to explore the breakdown mechanisms of torus attractors and multistability phenomena. The multistability includes the coexistence of multiple torus attractors and the coexistence of torus and chaotic attractors. In addition, we show that grazing bifurcations induce the destruction of torus attractors with the emergence of either chaotic attractors or strange nonchaotic attractors.