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

TL;DR

This paper introduces a universal method for constructing and analyzing recurrence networks from chaotic time series, enabling objective comparison and revealing attractor structures.

Contribution

A general, empirical framework for recurrence network analysis that links threshold selection to embedding dimension and applies to real-world data.

Findings

Critical threshold range is consistent across different chaotic series.

Degree distribution reflects attractor structure and is scale-invariant.

Method effectively detects regime transitions and estimates system dimensionality.

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.