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Asymmetric Spotty Patterns for the Gray–Scott Model in R2

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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 k1, k2 , there are asymmetric solutions with k1 large spots (type A) and k2 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.
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Document Type: Research Article

Publication date: January 1, 2003

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