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

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Network Science

Background:

• Chaotic time series analysis often lacks standardized methods for comparing different systems.
• Recurrence networks offer insights into dynamical systems but require robust construction techniques.

Purpose of the Study:

• To introduce a general, empirical method for constructing unweighted ε-recurrence networks from chaotic time series.
• To establish a uniform framework for the objective comparison of recurrence networks derived from diverse chaotic attractors.

Main Methods:

• Empirical selection of a critical threshold (εc) linked to the embedding dimension (M).
• Numerical identification of a critical range (Δε) applicable across various time series.
• Analysis of degree distribution and statistical scale invariance of constructed networks.

Main Results:

• A small, consistent critical range (Δε) was identified for random and chaotic time series.
• The degree distribution of the recurrence networks reflects attractor structure and exhibits scale invariance.
• Successful application in detecting dynamical regime transitions and identifying system dimensionality from limited data.

Conclusions:

• The proposed method provides a robust and objective framework for analyzing chaotic time series using recurrence networks.
• Recurrence network measures can effectively characterize dynamical systems and their properties.
• The method has practical applications in real-world data analysis and system identification.