STRANGE NONCHAOTIC ATTRACTORS AND COMPLICATED QUASI-PERIODIC CASCADES INDUCED BY BIFURCATIONS IN A DRY-FRICTION OSCILLATOR UNDER QUASI-PERIODIC EXCITATION

This paper explores the crossing bifurcation, switching-sliding and grazing-sliding bifurcations in a dry-friction oscillator on a moving belt under quasi-periodic excitation with two frequencies. We present a concrete method to approximate the largest Lyapunov exponent. By applying the method of some numerical experiments, we find that as bifurcation parameter varies, the system shows quite rich dynamical behaviors, including: (1) For crossing and switching-sliding bifurcations, there exists an alternating sequence of chaotic attractors, quasi-periodic toruses and strange nonchaotic attractors (SNAs), in which SNA exists between chaotic attractor and quasi-periodic torus via an evolution route of torus → SNA → chaos. (2) Grazing-sliding bifurcation triggers a direct transition from a pre-grazing three-torus quasi-periodic orbit to an SNA. Furthermore, we also observe torus-adding cascades and weak torus-adding cascades in quasi-periodic attractors. The unique properties of the observed SNAs are comprehensively validated by the largest Lyapunov exponent, rational approximation, phase sensitivity property, singular continuous spectrum analysis and separation of nearby trajectories.