Transient Chaos in Spatially Extended Systems

Ying-Cheng Lai, Tamás Tél

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Chaos is not restricted to systems without any spatial extension: it in fact occurs commonly in spatially extended dynamical systems that are most typically described by nonlinear partial differential equations (PDEs). If the patterns generated by such a system change randomly in time, we speak of spatiotemporal chaos, a kind of temporally chaotic pattern-forming process. If, in addition, the patterns are also spatially irregular, there is fully developed spatiotemporal chaos. In principle, the phase-space dimension of a spatially extended dynamical system is infinite. However, in practice, when a spatial discretization scheme is used to solve the PDE, or when measurements are made in a physical experiment with finite spatial resolution, the effective dimension of the phase space is not infinite but still high.

Original languageEnglish (US)
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages311-339
Number of pages29
DOIs
StatePublished - Jan 1 2011

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume173
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Keywords

  • Chaotic Attractor
  • Dimension Density
  • Escape Rate
  • Lyapunov Exponent
  • Stable Manifold

ASJC Scopus subject areas

  • Applied Mathematics

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