Transient Chaos in Spatially Extended Systems

Ying Cheng Lai, T. 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
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages311-339
Number of pages29
DOIs
Publication statusPublished - Jan 1 2011

Publication series

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

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Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Lai, Y. C., & Tél, T. (2011). Transient Chaos in Spatially Extended Systems. In Applied Mathematical Sciences (Switzerland) (pp. 311-339). (Applied Mathematical Sciences (Switzerland); Vol. 173). Springer. https://doi.org/10.1007/978-1-4419-6987-3_9