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Title: Stability analysis of turing patterns generated by the Schnakenberg model
Authors: Winter, M
Wei, J
Iron, D
Keywords: Turing instability
Nonlocal Eigenvalue Problem
Symmetric N-peaked solutions
Publication Date: 2004
Publisher: Springer
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:Mathematics
School of Information Systems, Computing and Mathematics Research Papers

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