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|Title:||Stability Analysis of Turing Patterns Generated by the Schnakenberg Model|
|Keywords:||Symmetric N-peaked solutions;Nonlocal Eigenvalue Problem;Turing instability|
|Citation:||J Math Biol 49 (2004), 358-390|
|Abstract:||We consider the following Schnakenberg model on the interval (−1, 1): ut = D1u − u + vu2 in (−1, 1), vt = D2v + B − vu2 in (−1, 1), u (−1) = u (1) = v (−1) = v (1) = 0, where D1 > 0, D2 > 0, B>0. We rigorously show that the stability of symmetric N−peaked steady-states can be reduced to computing two matrices in terms of the diffusion coefficients D1,D2 and the number N of peaks. These matrices and their spectra are calculated explicitly and sharp conditions for linear stability are derived. The results are verified by some numerical simulations.|
|Appears in Collections:||Dept of Mathematics Research Papers|
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