Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/565

 Title: Critical Threshold and Stability of Cluster Solutions for Large Reaction-Diffusion Systems in R Authors: Winter, MWei, J Keywords: Pattern Formation, Stability,Cluster Solutions, Reaction-Diffusion System, Catalytic Network, Publication Date: 2002 Publisher: SIAM Citation: SIAM J Math Anal 33 (2002), 1058-1089 Abstract: We study a large reaction-diffusion system which arises in the modeling of catalytic networks and describes the emerging of cluster states. We construct single cluster solutions on the real line and then establish their stability or instability in terms of the number N of components and the connection matrix. We provide a rigorous analysis around the single cluster solutions, which is new for systems of this kind. Our results show that for N\leq 4 the hypercycle system is linearly stable while for N\geq 5 the hypercycle system is linearly unstable. URI: http://bura.brunel.ac.uk/handle/2438/565 Appears in Collections: MathematicsSchool of Information Systems, Computing and Mathematics Research Papers

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