Mechanism for the Intermittent Route to Strange Nonchaotic Attractors

Details Mechanism for the Intermittent Route to Strange Nonchaotic Attractors Mechanism for the Intermittent Route to Strange Nonchaotic Attractors

2002-08-21

arxiv.org/abs/nlin/0208028v2

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 figures. Revised in Fig. 3. Submitted for publication in the Phys. Rev. Lett

Scientific paper

10.1103/PhysRevE.67.056203

Intermittent strange nonchaotic attractors (SNAs) appear typically in quasiperiodically forced period-doubling systems. As a representative model, we consider the quasiperiodically forced logistic map and investigate the mechanism for the intermittent route to SNAs using rational approximations to the quasiperiodic forcing. It is thus found that a smooth torus is transformed into an intermittent SNA via a phase-dependent saddle-node bifurcation when it collides with a new type of ``ring-shaped'' unstable set. Besides this intermittent transition, other transitions such as the interior, boundary, and band-merging crises may also occur through collision with the ring-shaped unstable sets. Hence the ring-shaped unstable sets play a central role for such dynamical transitions. Furthermore, these kinds of dynamical transitions seem to be ``universal,'' in the sense that they occur typically in a large class of quasiperiodically forced period-doubling systems.

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