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

We propose a general method for the construction and analysis of unweighted ε-recurrence networks from chaotic time series. The selection of the critical threshold ε_{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 Δε 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 nonsubjective 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 a limited number of points through recurrence network measures. The merits, limitations, and the potential applications of the proposed method are also highlighted.