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Spring 2007

March 05, 2007 (Monday)
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

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