Strange nonchaotic attractors in a class of quasiperiodically forced piecewise smooth systems

The existence of strange nonchaotic attractors (SNAs) and the associated mechanisms are studied in a class of quasiperiodically forced piecewise smooth systems. We show that the birth of SNAs is through interior crisis, basin boundary metamorphosis, discontinuous quasiperiodic orbits, and double bifurcation routes. Compared with the fractal, torus-doubling, and type-I intermittency routes, the four routes have more abundant dynamical phenomena, namely, the crisis-induced intermittency, the collision between attractors and the boundaries of fractal basin, the discontinuous quasiperiodic orbits, and the double bifurcation vertices. The characteristics of SNAs are described with the help of some qualitative and quantitative methods, such as the Lyapunov exponent, phase sensitivity function, critical exponent, and power spectrum.