Unstable Dimension Variability and Codimension-one Bifurcations of Two-dimensional Maps

Celso Grebogi, R. L. Viana, J. R. R. Barbosa

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Unstable dimension variability is a mechanism whereby an invariant set of a dynamical system, like a chaotic attractor or a strange saddle, loses hyperbolicity in a severe way, with serious consequences on the shadowability properties of numerically generated trajectories. In dynamical systems possessing a variable parameter, this phenomenon can be triggered by the bifurcation of an unstable periodic orbit. This Letter aims at discussing the possible types of codimension-one bifurcations leading to unstable dimension variability in a two-dimensional map, presenting illustrative examples and displaying numerical evidences of this fact by computing finite-time Lyapunov exponents. (C) 2004 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)244-251
Number of pages7
JournalPhysics Letters A
Volume321
DOIs
Publication statusPublished - 2004

Keywords

  • COUPLED CHAOTIC SYSTEMS
  • LYAPUNOV EXPONENTS
  • PERIODIC-ORBITS
  • SYNCHRONIZATION
  • ATTRACTORS
  • DYNAMICS
  • SETS

Cite this

Unstable Dimension Variability and Codimension-one Bifurcations of Two-dimensional Maps. / Grebogi, Celso; Viana, R. L.; Barbosa, J. R. R.

In: Physics Letters A, Vol. 321, 2004, p. 244-251.

Research output: Contribution to journalArticle

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AB - Unstable dimension variability is a mechanism whereby an invariant set of a dynamical system, like a chaotic attractor or a strange saddle, loses hyperbolicity in a severe way, with serious consequences on the shadowability properties of numerically generated trajectories. In dynamical systems possessing a variable parameter, this phenomenon can be triggered by the bifurcation of an unstable periodic orbit. This Letter aims at discussing the possible types of codimension-one bifurcations leading to unstable dimension variability in a two-dimensional map, presenting illustrative examples and displaying numerical evidences of this fact by computing finite-time Lyapunov exponents. (C) 2004 Elsevier B.V. All rights reserved.

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KW - ATTRACTORS

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KW - SETS

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