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|Title: ||On a Two Dimensional Reaction-Diffusion System with Hypercyclical Structure|
|Authors: ||Winter, M|
|Keywords: ||Pattern Formation, Stability,|
Point-Condensations, Reaction-Diffusion System, Catalytic Network, Hypercycle
|Publication Date: ||2000|
|Citation: ||Nonlinearity 13 (2000), 2005-2030|
|Abstract: ||We study a
hypercyclical reaction-diffusion system which arises in
the modeling of catalytic networks and describes the emerging of cluster states.
We construct single cluster solutions in full two-dimensional space
and then establish their stability or instability in terms of the number N of components.
We provide a rigorous analysis around the single cluster solutions, which
is new for systems of this kind.
Our results show that as N increases, the system becomes unstable.|
|Appears in Collections:||School of Information Systems, Computing and Mathematics Research Papers|
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