Power-laws in recurrence networks from dynamical systems

• Published in: Europhysics letters Vol. 98; no. 4; pp. 48001 - 48006
• Main Authors: Zou, Y., Heitzig, J., Donner, R. V., Donges, J. F., Farmer, J. D., Meucci, R., Euzzor, S., Marwan, N., Kurths, J.
• Format: Journal Article
• Language: English
• Published: EPS, SIF, EDP Sciences and IOP Publishing 01.05.2012
• Subjects: 05.45.Tp; 89.75.Da; 89.75.Hc
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/0295-5075/98/48001

Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in classical mechanics. In this letter, we demonstrate that recurrence networks obtained from various deterministic model systems as well as experimental data naturally display power-law degree distributions with scaling exponents γ that can be derived exclusively from the systems' invariant densities. For one-dimensional maps, we show analytically that γ is not related to the fractal dimension. For continuous systems, we find two distinct types of behaviour: power-laws with an exponent γ depending on a suitable notion of local dimension, and such with fixed γ=1.