title: 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. In phase space, recurrence plots 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.
authors.affiliation: Department of German Language and Linguistics, Humboldt-Universität zu Berlin, 10099 Berlin, Germany and Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu Berlin, 10115 Berlin, Germany and Cortex Project, INRIA Nancy Grand Est, 54602 Villers-les-Nancy, France.
authors.forename: Peter
authors.initials: P
authors.lastname: beim Graben
authors.affiliation: Cortex Project, INRIA Nancy Grand Est, 54602 Villers-les-Nancy, France.
authors.forename: Axel
authors.initials: A
authors.lastname: Hutt
mesh_terms: D000465:Algorithms; D001921:Brain / Q000502:physiology; D004569:Electroencephalography; D019277:Entropy; D006801:Humans; D008962:Models, Theoretical