Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/11551
Title: Power-laws in recurrence networks from dynamical systems
Authors: Zou, Y
Heitzig, J
Donner, RV
Donges, JF
Farmer, JD
Meucci, R
Euzzor, S
Marwan, N
Kurths, J
Issue Date: 2012
Publisher: EDP Sciences
Source: EPL : a letters journal exploring the frontiers of physics, 2012, v. 98, no. 4, 48001 How to cite?
Journal: EPL : a letters journal exploring the frontiers of physics 
Abstract: 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.
URI: http://hdl.handle.net/10397/11551
ISSN: 0295-5075
EISSN: 1286-4854
DOI: 10.1209/0295-5075/98/48001
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