Mechanism for new boundary crises in quasiperiodically forced systems

초록

As a representative model for the Poincare map of quasiperiodically forced oscillators, we consider. the quasiperiodically forced Henon map and investigate the mechanism for boundary crises. Using rational approximations to quasiperiodic forcing, we show that a new type of boundary crisis occurs for a nonchaotic attractor (smooth torus or strange nonchaotic attractor), as well as a chaotic attractor, through a collision with an invariant "ring-shaped" unstable set which has no counterpart in the unforced case. This new boundary crisis is in contrast to the "standard" boundary crisis that occurs via a collision with smooth unstable torus.

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