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Signatures of chaotic and stochastic dynamics uncovered with epsilon-recurrence networks
Stockholm University, Faculty of Science, Stockholm Resilience Centre.
Number of Authors: 3
2015 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 471, no 2183, 20150349Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2015. Vol. 471, no 2183, 20150349
Keyword [en]
time-series analysis, complex networks, chaotic dynamics, stochastic dynamics
National Category
Bioinformatics (Computational Biology) Computer Engineering
URN: urn:nbn:se:su:diva-124178DOI: 10.1098/rspa.2015.0349ISI: 000363982600007OAI: diva2:884952
Available from: 2015-12-17 Created: 2015-12-15 Last updated: 2015-12-17Bibliographically approved

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Donges, Jonathan F.
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Stockholm Resilience Centre
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