Strange nonchaotic attractors in the quasiperiodically
forced circle map
Ulrike Feudel
Max-Planck-Arbeitsgruppe Nichtlineare Dynamik an der Universität Potsdam
Am Neuen Palais 10, Geb. 19, D-14469 Potsdam, Germany
Strange nonchaotic attractors exhibit an intermediate behaviour between regular (quasiperiodic) motion and chaotic motion. These attractors are fractals in the phase space, that means they are strange in a geometrical sense. On the other hand one cannot observe a sensitive dependence on the initial conditions, that means they are not chaotic in a dynamical sense. These attractors are observed in quasiperiodically forced systems.
In the quasiperiodically forced circle map strange nonchaotic attractors can appear for nonlinearities far from the border to chaos. The destruction of a two-frequency quasiperiodic torus connected with the appearence of a strange nonchaotic attractor is described as a touch of a stable and an unstable torus. The transition between quasiperiodic and strange nonchaotic attractors as well as strange nonchaotic and chaotic attractors can be described by monitoring the evolution of snapshot attractors.
It is shown, that in the quasiperiodically forced circle map the form of the Arnol'd tongues of phase-locking changes and the high-order phase-locking states disappear. As a result the rotation number varies rather smoothly with the parameters.