Bubbling Bifurcation: Loss of Synchronization and Shadowing Breakdown in Complex Systems

Celso Grebogi, R. L. Viana, S. E. S. Pinto, S. R. Lopes, A. M. Batista, J. Kurths

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Abstract

Complex dynamical systems with many degrees of freedom may exhibit a wealth of collective phenomena related to high-dimensional chaos. This paper focuses on a lattice of coupled logistic maps to investigate the relationship between the loss of chaos synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization manifold. This has been confirmed by numerical diagnostics of synchronization and non-hyperbolic behavior, the latter using the statistical properties of finite-time Lyapunov exponents. (c) 2005 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)94-108
Number of pages14
JournalPhysics Review D
Volume206
DOIs
Publication statusPublished - 2005

Keywords

  • bubbling bifurcation
  • synchronization
  • shadowing breakdown
  • COUPLED MAP LATTICES
  • UNSTABLE DIMENSION VARIABILITY
  • CHAOTIC SYSTEMS
  • PHASE SYNCHRONIZATION
  • SPATIOTEMPORAL CHAOS
  • RIDDLED BASINS
  • OSCILLATORS
  • LONG
  • INTERMITTENCY
  • TRANSITIONS

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