Looking
for order within chaos: Locating and understanding coherent
structures within Kuramoto-Sivashinsky equation
Ruslan L. Davidchack
University of Leicester
In this
talk I will discuss our efforts to understand the properties of chaotic
solutions of the Kuramoto-Sivashinsky equation by locating and
analyzing coherent structures (equilibria, traveling waves, periodic
and relative periodic orbits) embedded within the chaotic
dynamics. Our approach for locating the coherent structures is
based on transforming the original equation in such a way that the
unstable structures are stabilized by the transformation. The
approach has proved very successful in low dimensional chaotic systems
and has now been extended to high dimensional flows such as discretized
PDEs. Using this approach we have found many coherent structures
within a moderately chaotic regime of the Kuramoto-Sivashinsky dynamics
and are now attempting to understand the chaotic dynamics in terms of
these structures.Time: 4:30 pm
Skiles 255
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OTHERWISE NOTED.