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 $Λ$ 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, $Λ$ changes sharply at the SNA to torus transition, as does the distribution of finite-time or N--step Lyapunov exponents, P(Λ_N).