Feigenbaum graphs: a complex network perspective of chaos.

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with...

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Autores principales:	Bartolo Luque, Lucas Lacasa, Fernando J Ballesteros, Alberto Robledo
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2011
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/da9f50d2850247c7b3750992e23e3b8b
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id	oai:doaj.org-article:da9f50d2850247c7b3750992e23e3b8b
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spelling	oai:doaj.org-article:da9f50d2850247c7b3750992e23e3b8b2021-11-18T06:46:36ZFeigenbaum graphs: a complex network perspective of chaos.1932-620310.1371/journal.pone.0022411https://doaj.org/article/da9f50d2850247c7b3750992e23e3b8b2011-01-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/21915254/pdf/?tool=EBIhttps://doaj.org/toc/1932-6203The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.Bartolo LuqueLucas LacasaFernando J BallesterosAlberto RobledoPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 6, Iss 9, p e22411 (2011)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Bartolo Luque Lucas Lacasa Fernando J Ballesteros Alberto Robledo Feigenbaum graphs: a complex network perspective of chaos.
description	The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.
format	article
author	Bartolo Luque Lucas Lacasa Fernando J Ballesteros Alberto Robledo
author_facet	Bartolo Luque Lucas Lacasa Fernando J Ballesteros Alberto Robledo
author_sort	Bartolo Luque
title	Feigenbaum graphs: a complex network perspective of chaos.
title_short	Feigenbaum graphs: a complex network perspective of chaos.
title_full	Feigenbaum graphs: a complex network perspective of chaos.
title_fullStr	Feigenbaum graphs: a complex network perspective of chaos.
title_full_unstemmed	Feigenbaum graphs: a complex network perspective of chaos.
title_sort	feigenbaum graphs: a complex network perspective of chaos.
publisher	Public Library of Science (PLoS)
publishDate	2011
url	https://doaj.org/article/da9f50d2850247c7b3750992e23e3b8b
work_keys_str_mv	AT bartololuque feigenbaumgraphsacomplexnetworkperspectiveofchaos AT lucaslacasa feigenbaumgraphsacomplexnetworkperspectiveofchaos AT fernandojballesteros feigenbaumgraphsacomplexnetworkperspectiveofchaos AT albertorobledo feigenbaumgraphsacomplexnetworkperspectiveofchaos
_version_	1718424449764556800

Feigenbaum graphs: a complex network perspective of chaos.

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