ABSTRACT
We propose recurrence plots (RPs) to characterize the stickiness of a typical area-preserving map with coexisting chaotic and regular orbits. The difference of the recurrence properties between quasiperiodic and chaotic orbits is revisited, which helps to understand the complex patterns of the corresponding RPs. Moreover, several measures from the recurrence quantification analysis are used to quantify these patterns. Among these measures, the recurrence rate, quantifying the percentage of black points in the plot, is applied to characterize the stickiness of a typical chaotic orbit. The advantage of the recurrence based method in comparison to other standard techniques is that it is possible to distinguish between quasiperiodic and chaotic orbits that are temporarily trapped in a sticky domain, from very short trajectories.
ACKNOWLEDGMENTS
The authors would like to thank Diego Pazó for very fruitful discussions. This work was supported by the International Helmholtz Institute for Super-computational Physics (MWFK Land Brandenburg), SPP 1114 (DFG), and the Promotionskolleg Behavioral and Cognitive Dynamics (Excellence Programme, Potsdam University). The constructive and careful comments and suggestions from the referees are also acknowledged.
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