TURING PATTERN FORMATION IN THE BRUSSELATOR MODEL WITH SUPERDIFFUSION

被引：84

作者：

Golovin, A. A. ^{[1
]}

Matkowsky, B. J. ^{[1
]}

Volpert, V. A.

机构：

[1] Northwestern Univ, Dept Engn Sci & Appl Math, Evanston, IL 60208 USA

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2008年 / 69卷 / 01期

关键词：

pattern formation; Brusselator; anomalous diffusion; superdiffusion; Turing instability;

D O I：

10.1137/070703454

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：251 / 272

页数：22

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