Better Recurrence Plots

In the previous post in the Lorenz63 series we used recurrence plots to get a qualitative feel for the type of behavior exhibited by a time series (stochastic, periodic, chaotic). Those were using the default colormap in matplotlib, and they seem to highlight the “holes” more than the “near returns” (at least to my eye). Here’s some improved ones that use the bone colormap and a threshold on the distance to better highlight the near returns.

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(a) Single Trajectory (b) Ensemble Mean Figure 1: Response of Lorenz 1963 model

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(a) Periodic Series (b) Stochastic Series Figure 2: Non-chaotic Series

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(a) A little smoothing (b) More smoothing (c) Even more smoothing Figure 3: Smoothing of a Lorenz 1963 trajectory

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