Description: One principal goal of the grant was to model and analyze the dynamics of spatially extended chaotic systems. One of the principal tools used in the analysis was KLTOOL, a computer package developed by the principal investigators for Karhunen-Loeve analysis. The package was used to analyze video data from a laboratory experiment on cellular flames. A second goal of the project was to analyze complex time series whose underlying dynamics may be low dimensionally chaotic. Particular emphasis was placed on systems of possible relevance to energy production and distribution. The work attempted to characterize low-dimensional aspects of the dynamics of a fluidized bed, in particular, a transition from periodic to irregular behavior. Finally, collaborators worked on aspects of targeting in chaotic dynamical systems. This work showed that it is possible to switch a moderately high-dimensional chaotic process rapidly between prespecified periodic saddle orbits embedding within the attractor. Additional work extended previously-developed algorithms for the highly accurate computation of stable manifolds of periodic saddle orbits, which is essential to the successful application of targeting algorithms.
Date: September 1, 1998
Creator: Kostelich, E.J. & Armbruster, H.D.
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