Recurrence analysis of strange nonchaotic dynamics

We present methods to detect the transitions from quasiperiodic to chaotic motion via strange nonchaotic attractors (SNAs). These procedures are based on the time needed by the system to recur to a previously visited state and a quantification of the synchronization of trajectories on SNAs. The applicability of these techniques is demonstrated by detecting the transition to SNAs or the transition from SNAs to chaos in representative quasiperiodically forced discrete maps. The fractalization transition to SNAs—for which most existing diagnostics are inadequate—is clearly detected by recurrence analysis. These methods are robust to additive noise, and thus can be used in analyzing experimental time series.