Phase-locking in quasiperiodically forced systems

摘要

We study the influence of a quasiperiodic force on the phase-locking structure in the circle map. We show that with increasing forcing the phase-locking regions change their shape from a tongue with monotonically increasing width to the shape of a leaf where the width first grows and then shrinks to values close to zero. The change in the shape is accompanied by a change of the bifurcation type along the boundary curves of the phase-locking regions. For small forcing there is a transition from two-to three-frequency motion, but for larger forcing the transition is from mio-frequency quasiperiodicity to a strange nonchaotic attractor.