Detecting recurrence domains of dynamical systems by symbolic dynamics

TL;DR

This paper introduces an algorithm that detects recurrence domains in complex dynamical systems using symbolic dynamics and recurrence plots, aiding in analyzing high-dimensional brain signals.

Contribution

The novel algorithm merges recurrence domains from time series data into phase space partitions using a rewriting grammar and entropy principles.

Findings

Effective detection of recurrence domains in high-dimensional brain signals

Revealed functional components of brain activity

Enhanced understanding of dynamical structures in complex systems

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.