Uniform framework for the recurrence-network analysis of chaotic time series

Abstract

We propose a general method for the construction and analysis of unweighted $\epsilon$ - recurrence networks from chaotic time series. The selection of the critical threshold ${\epsilon }_c$ in our scheme is done empirically and we show that its value is closely linked to the embedding dimension $M$. In fact, we are able to identify a small critical range $\Delta \epsilon$ numerically that is approximately the same for the random and several standard chaotic time series for a fixed $M$. This provides us a uniform framework for the non subjective comparison of the statistical measures of the recurrence networks constructed from various chaotic attractors. We explicitly show that the degree distribution of the recurrence network constructed by our scheme is characteristic to the structure of the attractor and display statistical scale invariance with respect to increase in the number of nodes $N$. We also present two practical applications of the scheme, detection of transition between two dynamical regimes in a time delayed system and identification of the dimensionality of the underlying system from real world data with limited number of points, through recurrence network measures. The merits, limitations and the potential applications of the proposed method have also been highlighted.

26 pages, 18 figures

References in corpus (9)

• Recurrence Plots for the Analysis of Complex Systems
• From time series to complex networks: the visibility graph
• Complex Network Approach for Recurrence Analysis of Time Series
• Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods
• Ambiguities in recurrence-based complex network representations of time series
• Analytical framework for recurrence-network analysis of time series
• Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods
• Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems
• A non subjective approach to the GP algorithm for analysing noisy time series

Cited by in corpus (13)

• Complex network approaches to nonlinear time series analysis
• Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions
• Measure for degree heterogeneity in complex networks and its application to recurrence network analysis
• Revisiting Evidence of Chaos in X-ray Light Curves: The Case of GRS 1915+105
• Recurrence network measures for hypothesis testing using surrogate data: application to black hole light curves
• Can recurrence networks show small world property?
• Recurrence measures and transitions in stock market dynamics
• Classification of Close Binary Stars Using Recurrence Networks
• Multiplex Recurrence Networks from multi-lead ECG data
• Quantifying information loss on chaotic attractors through recurrence networks
• Recurrence network analysis in a model tripartite quantum system
• Recurrence analysis of meteorological data from climate zones in India
• Degree weighted recurrence networks for the analysis of time series data