Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the Rössler System

In this paper, using the Poincaré section of the flow we numerically verify a generalization of a Pesin-like identity at the chaos threshold of the Rössler system, which is one of the most popular three-dimensional continuous systems. As Poincaré section points of the flow show similar behavior to t...

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Autores principales: Cetin, Kivanc, Afsar, Ozgur, Tirnakli, Ugur
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512731/
https://www.ncbi.nlm.nih.gov/pubmed/33265307
http://dx.doi.org/10.3390/e20040216
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author Cetin, Kivanc
Afsar, Ozgur
Tirnakli, Ugur
author_facet Cetin, Kivanc
Afsar, Ozgur
Tirnakli, Ugur
author_sort Cetin, Kivanc
collection PubMed
description In this paper, using the Poincaré section of the flow we numerically verify a generalization of a Pesin-like identity at the chaos threshold of the Rössler system, which is one of the most popular three-dimensional continuous systems. As Poincaré section points of the flow show similar behavior to that of the logistic map, for the Rössler system we also investigate the relationships with respect to important properties of nonlinear dynamics, such as correlation length, fractal dimension, and the Lyapunov exponent in the vicinity of the chaos threshold.
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spelling pubmed-75127312020-11-09 Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the Rössler System Cetin, Kivanc Afsar, Ozgur Tirnakli, Ugur Entropy (Basel) Article In this paper, using the Poincaré section of the flow we numerically verify a generalization of a Pesin-like identity at the chaos threshold of the Rössler system, which is one of the most popular three-dimensional continuous systems. As Poincaré section points of the flow show similar behavior to that of the logistic map, for the Rössler system we also investigate the relationships with respect to important properties of nonlinear dynamics, such as correlation length, fractal dimension, and the Lyapunov exponent in the vicinity of the chaos threshold. MDPI 2018-03-23 /pmc/articles/PMC7512731/ /pubmed/33265307 http://dx.doi.org/10.3390/e20040216 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Cetin, Kivanc
Afsar, Ozgur
Tirnakli, Ugur
Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the Rössler System
title Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the Rössler System
title_full Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the Rössler System
title_fullStr Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the Rössler System
title_full_unstemmed Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the Rössler System
title_short Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the Rössler System
title_sort generalized pesin-like identity and scaling relations at the chaos threshold of the rössler system
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512731/
https://www.ncbi.nlm.nih.gov/pubmed/33265307
http://dx.doi.org/10.3390/e20040216
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