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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. |
| URI: | 10.1007/s00285-003-0258-y
http://bura.brunel.ac.uk/handle/2438/556 |
| Appears in Collections: | Mathematics
School of Information Systems, Computing and Mathematics Research Papers
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