Power-laws in recurrence networks from dynamical systems
| Autor: | Zou, Y., Heitzig, J., Donner, R. V., Donges, J. F., Farmer, J. D., Meucci, R., Euzzor, S., Marwan, N., Kurths, J. |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Europhysics Letters 98, 48001 (2012) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1209/0295-5075/98/48001 |
| Popis: | 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 $\gamma=1$. Comment: 6 pages, 7 figures |
| Databáze: | arXiv |
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