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Signatures of chaotic and stochastic dynamics uncovered with epsilon-recurrence networks

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Details

Original languageEnglish
Article number20150349
JournalProceedings of the Royal Society A: Mathematical Physical and Engineering Sciences
Volume471
Issue number2183
DOIs
Publication statusPublished - 8 Nov 2015
Publication typeA1 Journal article-refereed

Abstract

An old and important problem in the field of nonlinear time-series analysis entails the distinction between chaotic and stochastic dynamics. Recently, e-recurrence networks have been proposed as a tool to analyse the structural properties of a time series. In this paper, we propose the applicability of local and global e-recurrence network measures to distinguish between chaotic and stochastic dynamics using paradigmatic model systems such as the Lorenz system, and the chaotic and hyper-chaotic Rossler system. We also demonstrate the effect of increasing levels of noise on these network measures and provide a real-world application of analysing electroencephalographic data comprising epileptic seizures. Our results show that both local and global e-recurrence network measures are sensitive to the presence of unstable periodic orbits and other structural features associated with chaotic dynamics that are otherwise absent in stochastic dynamics. These network measures are still robust at high noise levels and short data lengths. Furthermore, e-recurrence network analysis of the real-world epileptic data revealed the capability of these network measures in capturing dynamical transitions using short window sizes. e-recurrence network analysis is a powerful method in uncovering the signatures of chaotic and stochastic dynamics based on the geometrical properties of time series.

Keywords

  • time-series analysis, complex networks, chaotic dynamics, stochastic dynamics, TIME-SERIES ANALYSIS, COMPLEX NETWORK, SYSTEMS, NOISE, INFORMATION, TRANSITIONS, CENTRALITY, NONLINEARITY, DETERMINISM, QUANTIFIERS

Publication forum classification

Field of science, Statistics Finland