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Monday, March 13, 2006
11:00 AM - 12:00 PM
CNLS Conference Room (TA-3, Bldg 1690)

Seminar

Patterns on Growing Square Domains via Mode Interactions

Adela Comanici
University of Houston

We consider reaction-diffusion systems on growing square domains with Neumann boundary conditions (NBC). As suggested by numerical simulations, we study the simpler problem of mode interactions in steady-state bifurcation problems with D4+T2 symmetry, combined with the symmetry constraint imposed by NBC. We show that the transition between different types of squares can be generically continuous. Also, we show that transitions between squares and stripes can occur generically via a jump, via steady-states or via steady-states and time-periodic states. We point out some differences between stable patterns in the NBC problem and in the periodic boundary conditions problem. This is joint work with Martin Golubitsky.