Applied Math Seminar
Monday, January 24, 2000, 4:00pm, 120 Physics
Tasso J. Kaper (Boston University, Dept of Math)
Strong Pulse Interactions in Coupled Reaction-Diffusion Systems
Abstract:- A plethora of biological and chemical pattern formation
problems are modeled using coupled reaction-diffusion equations
of activator-inhibitor type. In 1993, the new phenomenon of self-
-replicating spots and pulses was discovered in the Gray-Scott model
and in a ferrocyanide reaction it models, by John Pearson and Harry
Swinney and collaborators. In this talk, we present an analysis of pulse
splitting. Furthermore, it turns out that the perturbation theory developed
for the Gray-Scott analysis can be extended in a natural way to analyze
a general class of coupled activator-inhibitor systems, including the
Gierer-Meinhart and Schnakenberg models, in order to determine whether
pulses attract or repel each other, and if they repel, whether they
also the undergo self-replication. The work may be classified as a
treatment of the moderately strong and strong pulse interaction problem.
This work is part of a larger collaborative project with Arjen Doelman,
Wiktor Eckhaus, Rob Gardner and my student Dave Morgan. We will conclude
with some open questions.
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