In this paper we study recurrence plots (RPs) for the simplest example of nontrivial recurrences, namely in the case of a quasiperiodic motion. This case can be still studied analytically and constitutes a link between simple periodic and more complicated chaotic dynamics. Since we deal with nontrivial recurrences, the size of the neighborhood ¿ to which the trajectory must recur, is larger than zero. This leads to a nonzero width of the lines, which we determine analytically for both periodic and quasiperiodic motion. The understanding of such microscopic structures is important for choosing an appropriate threshold ¿ to analyze experimental data by means of RPs.
- recurrence plot
- analytic description
- quasiperiodic motion
- nontrivial recurrence
Zou, Y., Thiel, M., Romano , M. C., & Kurths, J. (2007). Analytical description of recurrence plots of dynamical systems with nontrivial recurrences. International Journal of Bifurcation and Chaos, 17(12), 4273-4283. https://doi.org/10.1142/S0218127407019949