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Phase Dynamics, Phase Resetting, Correlation Functions and Coupled Map Lattices

  • Raymond Kapral
  • Merk-Na Chee
  • Stuart G. Whittington
  • Gian-Luca Oppo
Part of the NATO ASI Series book series (NSSB, volume 208)

Abstract

Some of the richest dynamical phenomena occur in both space and time. In view of the substantial developments that have taken place in the understanding of the onset of chaos in spatially homogeneous systems, which are described by systems of ordinary differential equations, there is some hope that parallel developments may take place in the study of spatially distributed systems that are usually described by partial differential equations. It is safe to say that this goal has not yet been achieved. The problem is twofold: not only are the phenomena diverse so that a set of organizing features like the major routes to chaos in spatially homogeneous systems has yet to be discovered, but some of the most useful nonlinear dynamics techniques, like surface of section plots, fractal dimensions and Lyapunov numbers, lose some of their utility for these high-dimensional systems. While all of the above tools can and have been brought to bear on the problem of spatio-temporal structure there is no one definitive diagnostic method.

Keywords

Domain Growth Phase Reset Chemical Wave Wave Propagation Process Pattern Formation Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • Raymond Kapral
    • 1
  • Merk-Na Chee
    • 1
  • Stuart G. Whittington
    • 1
  • Gian-Luca Oppo
    • 2
  1. 1.Chemical Physics Theory Group Department of ChemistryUniversity of TorontoTorontoCanada
  2. 2.Department of PhysicsDrexel UniversityPhiladelphiaUSA

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