Volume 98, Number 4, May 2012
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||23 May 2012|
Power-laws in recurrence networks from dynamical systems
Department of Physics, East China Normal University - Shanghai, China
2 Potsdam Institute for Climate Impact Research - Potsdam, Germany, EU
3 Department of Electronic and Information Engineering, The Hong Kong Polytechnic University Kowloon, Hong Kong
4 Santa Fe Institute - Santa Fe, NM, USA
5 Department of Physics, Humboldt University - Berlin, Germany, EU
6 Department of Physics, University of Florence - Florence, Italy, EU
7 Institute for Complex Systems and Mathematical Biology, University of Aberdeen - Aberdeen, UK, EU
Accepted: 18 April 2012
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.
PACS: 89.75.Hc – Networks and genealogical trees / 05.45.Tp – Time series analysis / 89.75.Da – Systems obeying scaling laws
© EPLA, 2012
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