Year: 2012
Type: article
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.
Source: Europhysics Letters (EPL)
Authors: Y. Zou, J. Heitzig, R. V. Donner, J. F. Donges, J. D. Farmer, R. Meucci, S. Euzzor, N. Marwan, J. Kurths
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2137703106