期刊
出版社
ROYAL SOC
DOI: 10.1098/rspa.2015.0349
关键词
time-series analysis; complex networks; chaotic dynamics; stochastic dynamics
资金
- 3DNeuroN project in the European Union's Seventh Framework Programme, Future and Emerging Technologies [296590]
- Tekes Human Spare Parts project
- Stordalen foundation (via the PB.net initiative)
- BMBF
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.
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