Multistability and nonsmooth bifurcations in the quasiperiodically forced circle map

Details Multistability and nonsmooth bifurcations in the quasiperiodically forced circle map Multistability and nonsmooth bifurcations in the quasiperiodically forced circle map

2000-05-16

arxiv.org/abs/nlin/0005032v1

Nonlinear Sciences

Chaotic Dynamics

25 pages, 22 colored figures in reduced quality, submitted to Int. J. of Bifurcation and Chaos, a supplementary website (htt

Scientific paper

It is well-known that the dynamics of the Arnold circle map is phase-locked in regions of the parameter space called Arnold tongues. If the map is invertible, the only possible dynamics is either quasiperiodic motion, or phase-locked behavior with a unique attracting periodic orbit. Under the influence of quasiperiodic forcing the dynamics of the map changes dramatically. Inside the Arnold tongues open regions of multistability exist, and the parameter dependency of the dynamics becomes rather complex. This paper discusses the bifurcation structure inside the Arnold tongue with zero rotation number and includes a study of nonsmooth bifurcations that happen for large nonlinearity in the region with strange nonchaotic attractors.

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