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|Title:||On a Two Dimensional Reaction-Diffusion System with Hypercyclical Structure|
|Keywords:||Pattern Formation, Stability,;Point-Condensations, Reaction-Diffusion System, Catalytic Network, Hypercycle|
|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:||Dept of Mathematics Research Papers|
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