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Turing Pattern Formation in the Brusselator Model with Superdiffusion
SIAM J. Appl. Math. Volume 69, Issue 1, pp. 251-272 (2008)
Published October 13, 2008
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The effect of superdiffusion on pattern formation and pattern selection in the Brusselator model is studied. Our linear stability analysis shows, in particular, that, unlike the case of normal diffusion, the Turing instability can occur even when diffusion of the inhibitor is slower than that of the initiator. A weakly nonlinear analysis yields a system of amplitude equations, analysis of which predicts parameter regimes where hexagons, stripes, and their coexistence are expected. Numerical computations of the original Brusselator model near the stability boundaries confirm the results of the analysis. In addition, further from the stability boundaries, we find a regime of self-replicating spots.
©2008 Society for Industrial and Applied Mathematics| History: | Received September 21, 2007; accepted June 11, 2008; published October 13, 2008 |
| Permalink: | http://dx.doi.org/10.1137/070703454 |
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