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|Title: ||Critical Threshold and Stability of Cluster Solutions for Large Reaction-Diffusion Systems in R|
|Authors: ||Winter, M|
|Keywords: ||Pattern Formation, Stability,|
Cluster Solutions, Reaction-Diffusion System, Catalytic Network,
|Publication Date: ||2002|
|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.|
|Appears in Collections:||School of Information Systems, Computing and Mathematics Research Papers|
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