Birth of strange nonchaotic attractors in a piecewise linear oscillator

Abstract

Nonsmooth systems are widely encountered in engineering fields. They have abundant dynamical phenomena, including some results on the complex dynamics in such systems under quasiperiodically forced excitations. In this work, we consider a quasiperiodically forced piecewise linear oscillator and show that strange nonchaotic attractors (SNAs) do exist in such nonsmooth systems. The generation and evolution mechanisms of SNAs are discussed. The torus-doubling, fractal, bubbling, and intermittency routes to SNAs are identified. The strange properties of SNAs are characterized with the aid of the phase sensitivity function, singular continuous spectrum, rational frequency approximation, and the path of the partial Fourier sum of state variables in a complex plane. The nonchaotic properties of SNAs are verified by the methods of maximum Lyapunov exponent and power spectrum.