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

Identifieur interne : 001374 ( Main/Exploration ); précédent : 001373; suivant : 001375

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

Auteurs : Peter Beim Graben [Allemagne] ; Axel Hutt [France]

Source :

Physical Review Letters [ 0031-9007 ] ; 2013.

RBID : Hal:hal-00847164

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.

Url:

https://hal.inria.fr/hal-00847164

DOI: 10.1103/PhysRevLett.110.154101

Affiliations:

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<front><div type="abstract" xml:lang="en">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.</div>
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Detecting metastable states of dynamical systems by recurrence-based symbolic dynamics

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

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Abstract

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