Deconstructing Spatiotemporal Chaos Using Local Symbolic Dynamics

Abstract

We find that the global symbolic dynamics of a diffusively coupled map lattice (CML) is well approximated by a very small local model for weak to moderate coupling strengths. A local symbolic model is a truncation of the full symbolic model to one that considers only a single element and a few neighbors. Using interval analysis we give rigorous results for a range of coupling strengths and different local model widths. Examples are presented of extracting a local symbolic model from data and of controlling spatiotemporal chaos.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 2008
Accession Number
ADA505938

Entities

People

  • Ned J. Corron
  • Shawn D. Pethel

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Boundaries
  • Complex Systems
  • Couplings
  • Data Sets
  • Diffusion
  • Digital Computers
  • Dynamic Range
  • Dynamics
  • Engineering
  • Information Operations
  • Intervals
  • Iterations
  • Mathematics
  • Military Research
  • Sequences
  • Truncation

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Mathematical Modeling and Probability Theory.
  • Neural Network Machine Learning.