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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