Mechanism for the band-merging route to strange nonchaotic attractors in quasiperiodically forced systems

초록

As a representative model for quasiperiodically forced period-doubling systems, we consider the quasiperiodically forced Henon map and investigate the dynamical mechanism for the band-merging route to intermittent strange nonchaotic attractors (SNAs). Using the rational approximation to quasiperiodic forcing, we show that a band-merging transition from a two-band smooth torus to a single-band intermittent SNA occurs when the smooth torus collides with a ring-shaped unstable set which has no counterpart in the unforced case. The mechanism for the band-merging transition to intermittent SNAs is also confirmed in the quasiperiodically forced Toda oscillator. In addition to inducing the transition to SNAs, such a band-merging mechanism is a direct cause for the truncation of the torus-doubling sequence.

키워드