Intermittency Route to Strange Nonchaotic Attractors

Abstract

Strange nonchaotic attractors (SNA) arise in quasiperiodically driven systems in the neighborhood of a saddle-node bifurcation whereby a strange attractor is replaced by a periodic (torus) attractor. This transition is accompanied by Type-I intermittency. The largest nontrivial Lyapunov exponent $\ensuremath{\Lambda}$ is a good order parameter for this route from chaos to SNA to periodic motion: the signature is distinctive and unlike that for other routes to SNA. In particular, $\ensuremath{\Lambda}$ changes sharply at the SNA to torus transition, as does the distribution of finite-time or $N$-step Lyapunov exponents, $P({\ensuremath{\Lambda}}_{N})$.