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| Title: | Symmetric and Asymmetric Multiple Clusters In a Reaction-Diffusion System |
| Authors: | Winter, M
Wei, J |
| Keywords: | Multiple clusters
singular perturbation
Turing instability |
| Publication Date: | 2007 |
| Publisher: | Birkhaeuser, Basel |
| Citation: | NoDEA Nonlinear differ. equ. appl. 14 (2007), 787-823 |
| Abstract: | We consider the Gierer-Meinhardt system in
the interval (-1,1) with Neumann boundary
conditions for small diffusion constant
of the activator and finite diffusion
constant of the inhibitor.
A cluster is a combination of several spikes
concentrating at the same point.
In this paper, we rigorously show the existence
of symmetric and asymmetric multiple clusters.
This result is new for systems and seems not
to occur for single equations.
We reduce the problem to the computation of two
matrices which depend on the coefficient of
the inhibitor as well as the number of different clusters and the number of spikes within each
cluster. |
| URI: | http://bura.brunel.ac.uk/handle/2438/1517 |
| Appears in Collections: | Mathematics
School of Information Systems, Computing and Mathematics Research Papers
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