Interruption of torus doubling bifurcation and genesis of strange nonchaotic attractors in a quasiperiodically forced map: Mechanisms and their characterizations - art. no. 026219

A simple quasiperiodically forced one-dimensional cubic map is shown to exh ibit very many types of routes to chaos via strange nonchaotic attractors ( SNAs) in a two-parameter (A-f) space. The routes include transitions to cha os via SNAs from both a one-frequency torus and a period-doubled torus. In the former case, we identify the fractalization and type-I intermittency ro utes. In the latter case, we point out that at least four distinct routes f or the truncation of the torus-doubling bifurcation and the creation of SNA s occur in this model. In particular, the formation of SNAs through Heagy-H ammel, fractalization, and type-III intermittent mechanisms is described. I n addition, it has been found that in this system there are some regions in the parameter space where a dynamics involving a sudden expansion of the a ttractor, which tames the growth of period-doubling bifurcation, takes plac e, creating the SNA. The SNAs created through different mechanisms are char acterized by the behavior of the Lyapunov exponents and their variance, by the estimation of the phase sensitivity exponent, and through the distribut ion of-finite-time Lyapunov exponents.