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International Journal of Bifurcation and Chaos, 21(4), 1065–1075 (2011) DOI:10.1142/S0218127411029045
Local Minima-based Recurrence Plots for Continuous Dynamical Systems
A. Schultz, Y. Zou, N. Marwan, M. T. TurveyA major issue in using recurrence plots to study dynamical systems is the choice of neighborhood size for thresholding the distance matrix that creates the plot. This is particularly important for continuous dynamical systems as temporal correlations of the trajectory might provide redundant information for recurrence analysis. We suggest an alternative procedure for creating recurrence plots (RPs) using the local minima provided by the distance profile, which more or less corresponds to the recurrence information in the orthogonal direction. The local minima-based thresholding yields a clean RP of minimized line thickness, that is compared to the plot obtained by standard radius-based method for thresholding. New definitions of line segments arising from the local minima-based method are outlined, which yield consistent results with those derived from standard methods. Our preliminary comparison suggests that the newly introduced thresholding technique is more sensitive to small changes in a system's dynamics. We demonstrate our method by the chaotic Lorenz system without the loss of generality.
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