Abstract for March 21, 2006

Arnd Scheel (IMA): Periodic patterns: modulations, perturbations, and bifurcation

Sand ripples, animal coat patterns, or surface waves in fluid convection --- the regularity of spatio-temporally periodic patterns strikes us when the complexity of the system seems to predict incoherence. Motivated by chemical and biological patterns, we study oscillatory patterns in reaction-diffusion systems. The talk will lead us through old and recent results, from existence and bifurcations of wave trains with periodic boundary conditions, modulations of wave numbers and pattern selection in large domains, to the role of impurities and boundary conditions. Most of the results strive for a unified view on generic behavior, which would give us insight into the dynamics of complex systems when little is known about the underlying equations.

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