Intermittency Route to Strange Nonchaotic Attractors

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 $\mathrm{\Lambda }$ 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, $\mathrm{\Lambda }$ changes sharply at the SNA to torus transition, as does the distribution of finite-time or N–step Lyapunov exponents, P(\Lambda_N).