Detecting recurrence domains of dynamical systems by symbolic dynamics

Abstract

We propose an algorithm for the detection of recurrence domains of complex dynamical systems from time series. Our approach exploits the characteristic checkerboard texture of recurrence domains exhibited in recurrence plots (RP). In phase space, RPs yield intersecting balls around sampling points that could be merged into cells of a phase space partition. We construct this partition by a rewriting grammar applied to the symbolic dynamics of time indices. A maximum entropy principle defines the optimal size of intersecting balls. The final application to high-dimensional brain signals yields an optimal symbolic recurrence plot revealing functional components of the signal.

Accepted for Physical Review Letters; 10 pages, 2 figures

References in corpus (3)

• Line Structures in Recurrence Plots
• Mental States as Macrostates Emerging from EEG Dynamics
• Multiple phases in stochastic dynamics: geometry and probabilities

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