Power-laws in recurrence networks from dynamical systems

Y. Zou, J. Heitzig, R. V. Donner, J. F. Donges, J. D. Farmer, R. Meucci, S. Euzzor, N. Marwan, J. Kurths

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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 gamma 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

Original languageEnglish
Article number48001
Number of pages6
JournalEurophysics Letters
Issue number4
Publication statusPublished - May 2012


  • pseudoperiodic time-series
  • complex networks
  • strange attractors
  • chaos
  • behavior

Cite this

Zou, Y., Heitzig, J., Donner, R. V., Donges, J. F., Farmer, J. D., Meucci, R., Euzzor, S., Marwan, N., & Kurths, J. (2012). Power-laws in recurrence networks from dynamical systems. Europhysics Letters, 98(4), [48001]. https://doi.org/10.1209/0295-5075/98/48001