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Title: On a Hypercycle System with Nonlinear Rate
Authors: Winter, M
Wei, J
Keywords: Pattern Formation, Stability,
Point-Condensations, Reaction-Diffusion System, Catalytic Network, Hypercycle
Publication Date: 2001
Publisher: International Press
Citation: Meth Appl Anal 8 (2001), 257-278
Abstract: We study an (N+1)-hypercyclical reaction-diffusion system with nonlinear reaction rate n. It is shown that there exists a critical threshold N_0 such that for N\leq N_0 the system is stable while for N> N_0 it becomes unstable. It is also shown that for large reaction rate n, N_0 remains a constant: in fact for n \geq n_0 \sim 3.35, N_0=5 and for n < n_0 \sim 3.35, N_0=4. Some more general reaction-diffusion systems of N+1 equations are also considered.
Appears in Collections:Mathematical Science
Dept of Mathematics Research Papers

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