Horizontal visibility graphs generated by type-I intermittency

Núñez, Ángel M. and Luque Serrano, Bartolome and Lacasa Saiz de Arce, Lucas and Gómez Pérez, Jose Patricio and Robledo, Alberto (2013). Horizontal visibility graphs generated by type-I intermittency. "PHYSICAL REVIEW E", v. 87 (n. 5); pp.. ISSN 1539-3755. https://doi.org/10.1103/PhysRevE.87.052801.

Description

Title: Horizontal visibility graphs generated by type-I intermittency
Author/s:
  • Núñez, Ángel M.
  • Luque Serrano, Bartolome
  • Lacasa Saiz de Arce, Lucas
  • Gómez Pérez, Jose Patricio
  • Robledo, Alberto
Item Type: Article
Título de Revista/Publicación: PHYSICAL REVIEW E
Date: 2013
ISSN: 1539-3755
Volume: 87
Subjects:
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Matemática Aplicada y Estadística [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associatedHVgraphs.We showhowthe alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics.We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

More information

Item ID: 29153
DC Identifier: http://oa.upm.es/29153/
OAI Identifier: oai:oa.upm.es:29153
DOI: 10.1103/PhysRevE.87.052801
Deposited by: Memoria Investigacion
Deposited on: 07 Aug 2014 16:28
Last Modified: 22 Sep 2014 11:44
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