Crisis-induced unstable dimension variability in a dynamical system

Geraldo T. Kubo, Ricardo L. Viana, Sergio R. Lopes, Celso Grebogi

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Unstable dimension variability is an extreme form of non-hyperbolic behavior in chaotic systems whose attractors have periodic orbits with a different number of unstable directions. We propose a new mechanism for the onset of unstable dimension variability based on an interior crisis, or a collision between a chaotic attractor and an unstable periodic orbit. We give a physical example by considering a high-dimensional dissipative physical system driven by impulsive periodic forcing. (C) 2008 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)5569-5574
Number of pages6
JournalPhysics Letters A
Volume372
Issue number34
Early online date28 Jun 2008
DOIs
Publication statusPublished - 18 Aug 2008

Keywords

  • deterministic chaotic systems
  • bifurcation
  • exponent

Cite this

Crisis-induced unstable dimension variability in a dynamical system. / Kubo, Geraldo T.; Viana, Ricardo L.; Lopes, Sergio R.; Grebogi, Celso.

In: Physics Letters A, Vol. 372, No. 34, 18.08.2008, p. 5569-5574.

Research output: Contribution to journalArticle

Kubo, Geraldo T. ; Viana, Ricardo L. ; Lopes, Sergio R. ; Grebogi, Celso. / Crisis-induced unstable dimension variability in a dynamical system. In: Physics Letters A. 2008 ; Vol. 372, No. 34. pp. 5569-5574.
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