Power-laws in recurrence networks from dynamical systems
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 recu...
| Main Authors: | , , , , , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2012
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| _version_ | 1797105364725923840 |
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| author | Zou, Y Heitzig, J Donner, R Donges, J Farmer, J Meucci, R Euzzor, S Marwan, N Kurths, J |
| author_facet | Zou, Y Heitzig, J Donner, R Donges, J Farmer, J Meucci, R Euzzor, S Marwan, N Kurths, J |
| author_sort | Zou, Y |
| collection | OXFORD |
| description | 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 $\gamma=1$. |
| first_indexed | 2024-03-07T06:46:28Z |
| format | Journal article |
| id | oxford-uuid:fb0220d6-857c-489b-8668-67e521d2f7bf |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:46:28Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:fb0220d6-857c-489b-8668-67e521d2f7bf2022-03-27T13:10:48ZPower-laws in recurrence networks from dynamical systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fb0220d6-857c-489b-8668-67e521d2f7bfEnglishSymplectic Elements at Oxford2012Zou, YHeitzig, JDonner, RDonges, JFarmer, JMeucci, REuzzor, SMarwan, NKurths, JRecurrence 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 $\gamma=1$. |
| spellingShingle | Zou, Y Heitzig, J Donner, R Donges, J Farmer, J Meucci, R Euzzor, S Marwan, N Kurths, J Power-laws in recurrence networks from dynamical systems |
| title | Power-laws in recurrence networks from dynamical systems |
| title_full | Power-laws in recurrence networks from dynamical systems |
| title_fullStr | Power-laws in recurrence networks from dynamical systems |
| title_full_unstemmed | Power-laws in recurrence networks from dynamical systems |
| title_short | Power-laws in recurrence networks from dynamical systems |
| title_sort | power laws in recurrence networks from dynamical systems |
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