Strange nonchaotic attractors in a nonsmooth dynamical system

Abstract

Strange nonchaotic attractors (SNAs) have fractal geometric structure, but are nonchaotic in the dynamical sense. Since Grebogi et al. discovered SNA in 1984, it has become one of the important topics in nonlinear dynamics. Now, the study of SNAs has been mainly confined to smooth dynamics with quasiperiodic excitation or random excitation. In this paper, we consider a class of single-degree-of-freedom gear dynamical system with quasiperiodic forcing. We show that the gear transmission system can be modeled as a three-dimensional piecewise linear system, which belongs to a typical class of nonsmooth system. We then show that SNAs do exist in such nonsmooth dynamical system with quasiperiodic force. The dynamical behavior of the nonsmooth system is analyzed as a parameter is varied. The dynamics is analyzed through phase diagrams and bifurcation diagrams, Lyapunov exponents, singular continuous power spectrum, phase sensitivity of time series and rational approximations.