Chaotic transients in spatially extended systems

Tamas Tel, Ying-Cheng Lai

Research output: Contribution to journalLiterature review

88 Citations (Scopus)

Abstract

Different transient-chaos related phenomena of spatiotemporal systems are reviewed. Special attention is paid to cases where spatiotemporal chaos appears in the form of chaotic transients only. The asymptotic state is then spatially regular. In systems of completely different origins, ranging from fluid dynamics to chemistry and biology, the average lifetimes of these spatiotemporal transients are found, however, to grow rapidly with the system size, often in an exponential fashion. For sufficiently large spatial extension, the lifetime might turn out to be larger than any physically realizable time. There is increasing numerical and experimental evidence that in many systems such transients mask the real attractors. Attractors may then not be relevant to certain types of spatiotemporal chaos, or turbulence. The observable dynamics is governed typically by a high-dimensional chaotic saddle. We review the origin of exponential scaling of the transient lifetime with the system size, and compare this with a similar scaling with system parameters known in low-dimensional problems. The effect of weak noise on such supertransients is discussed. Different crisis phenomena of spatiotemporal systems are presented and fractal properties of the chaotic saddles underlying high-dimensional supertransients are discussed. The recent discovery according to which turbulence in pipe flows is a very long lasting transient sheds new light on chaotic transients in other spatially extended systems. (C) 2008 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)245-275
Number of pages31
JournalPhysics Reports
Volume460
Issue number6
Early online date13 Feb 2008
DOIs
Publication statusPublished - May 2008

Keywords

  • transient chaos
  • spatiotemporal dynamical systems
  • supertransients
  • chaotic saddle
  • turbulence
  • pipe flow
  • coupled-map lattices
  • Kuramoto-Sivashinsky equation
  • fractal basin boundaries
  • reaction-diffusion model
  • dynamical-systems
  • spatiotemporal chaos
  • pipe-flow
  • shear flows
  • turbulence transition
  • phase synchronization

Cite this