Border-collision bifurcation route to strange nonchaotic attractors in the piecewise linear normal form map

Abstract

Abstract A new route to strange nonchaotic attractors (SNAs) is investigated in a quasiperiodically driven nonsmooth map. It is shown that the smooth quasiperiodic torus becomes nonsmooth (continuous and non-differentiable) due to the border-collision bifurcation of the torus. The nonsmooth torus gets extremely fractal and becomes a strange nonchaotic attractor and it is termed the border-collision bifurcation route to SNAs. A novel feature of this route is that SNAs are abundant and the size of SNAs makes up about 40% of the given regions. These SNAs are identified by the Lyapunov exponents and the phase sensitivity exponents and they are also characterized by the singular-continuous spectrum and distribution of finite-time Lyapunov exponents. The distribution of local Lyapunov exponents has its maximum at a relatively small negative value, which contributes largely to lead to the abundance of SNAs.