2012/03/15 by Y. Zou, J. Heitzig, R. V. Donner +6 · 1 citation
Physics and Astronomy · #Chaos control and synchronization #Complex Network Analysis Techniques #Degree (music) #Dynamical systems theory #Exponent #Fractal #Nonlinear dynamical systems #Nonlinear system #Recurrence quantification analysis #Series (stratigraphy) #Statistical Mechanics and Entropy #nlin.CD
paper · pdf · doi:10.1209/0295-5075/98/48001
published as Europhysics Letters 98, 48001 (2012) · 6 pages, 7 figures
arxiv created 2012/03/15 · openalex publication_date 2012/05/01 · arxiv updated 2016/04/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.