Strange non-chaotic attractor in a quasiperiodically forced circle map

Abstract We show that in the quasiperiodically forced circle map strange non-chaotic attractors can appear for non-linearities far from the border of chaos. The destruction of a two-frequency quasiperiodic torus connected with the appearance of a strange non-chaotic attractor is described in detail. This strange non-chaotic attractor is characterized by logarithmically slow diffusion of the phase. It is shown that in this regime the high-order phase-locking states disappear and the rotation number varies rather smoothly with the parameters.

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