Detecting metastable states of dynamical systems by recurrence-based symbolic dynamics

Peter Beim Graben 1 Axel Hutt 2
2 NEUROSYS - Analysis and modeling of neural systems by a system neuroscience approach
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
Abstract : We propose an algorithm for the detection of recurrence domains of complex dynamical sys- tems 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 parti- tion 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.
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Peter Beim Graben, Axel Hutt. Detecting metastable states of dynamical systems by recurrence-based symbolic dynamics. Physical Review Letters, American Physical Society, 2013, 110, pp.154101. ⟨10.1103/PhysRevLett.110.154101⟩. ⟨hal-00847164⟩

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