Bifurcations and transitions in the quasiperiodically driven logistic map

Details Bifurcations and transitions in the quasiperiodically driven logistic map Bifurcations and transitions in the quasiperiodically driven logistic map

2001-05-08

arxiv.org/abs/nlin/0105014v1

Nonlinear Sciences

Chaotic Dynamics

17 Pages, 8 Figures(four figures are in ps format and four figures are in gif format

Scientific paper

We discuss several bifurcation phenomena that occur in the quasiperiodically driven logistic map. This system can have strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors; on SNAs the dynamics is aperiodic, but the largest Lyapunov exponent is nonpositive. There are a number of different transitions that occur here, from periodic attractors to SNAs, from SNAs to chaotic attractors, etc. We describe some of these transitions by examining the behavior of the largest Lyapunov exponent, distributions of finite time Lyapunov exponents and the invariant densities in the phase space.

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