Controlling Turbulence in Reaction Diffusion Systems
Abstract
We propose local symbolic models as a practical tool for understanding high-dimensional spatiotemporal chaos in reaction-diffusion systems modeled by coupled map lattices (CMLs). A local symbolic model is a truncation of the full symbolic dynamics to one that considers only a single element and a few neighbors. Local symbolic models can be applied element by element to a large lattice to build up an approximate picture of the global dynamics. Whereas the difficulty of finding the exact global symbolic dynamics increases exponentially with lattice size, the difficulty of the approximation presented here increases linearly at worst. The many uses of symbolic dynamics for one-dimensional maps, including control and targeting, are thus made practical for lattices. We explore the efficacy of the concatenated local model approach and give an example of controlling an arbitrary pattern in a CML using only small perturbations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 2006
- Accession Number
- ADA481913
Entities
People
- Ned J. Corron
- Shawn D. Pethel