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