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Tasso J. Kaper : Strong Pulse Interactions in Coupled Reaction-Diffusion Systems

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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