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Title: Asymmetric spotty patterns for the Gray-Scott model in R^2
Authors: Winter, M
Wei, J
Keywords: Asymmetric patterns; Spotty solutions;Self-replication; Reaction-diffusion system
Issue Date: 2003
Publisher: Blackwell
Citation: Stud Appl Math 110(2003): 63-102
Abstract: In this paper, we rigorously prove the existence and stability of asymmetric spotty patterns for the Gray-Scott model in a bounded two dimensional domain. We show that given any two positive integers k_1,\,k_2, there are asymmetric solutions with k_1 large spots (type A) and k_2 small spots (type B). We also give conditions for their location and calculate their heights. Most of these asymmetric solutions are shown to be unstable. However, in a narrow range of parameters, asymmetric solutions may be stable.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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