Power-laws in recurrence networks from dynamical systems
Authors: Zou Y., Heitzig J., Donner R.V., Donges J.F., Farmer J.D., Meucci R., Euzzor S., Marwan N., Kurths J.
Autors Affiliation: Department of Physics, East China Normal University, Shanghai, China; Potsdam Institute for Climate Impact Research, Potsdam, Germany; Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong; Santa Fe Institute, Santa Fe, NM, United States; Department of Physics, Humboldt University, Berlin, Germany; Department of Physics, University of Florence, Florence, Italy; Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen, United Kingdom
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 gamma that can be derived exclusively from the systems\’ invariant densities. For one-dimensional maps, we show analytically that ? is not related to the fractal dimension. For continuous systems, we find two distinct types of behaviour: power-laws with an exponent gamma depending on a suitable notion of local dimension, and such with fixed gamma=1. Copyright (C) EPLA, 2012
Volume: 98 (4) Pages from: 48001-1 to: 48001-6
KeyWords: Pseudoperiodic time-series; Complex networks; Strange attractors; Chaos; BehaviorDOI: 10.1209/0295-5075/98/48001