Pattern formation in three-dimensional reaction-diffusion systems

被引:76
作者
Callahan, TK
Knobloch, E [1 ]
机构
[1] Univ Calif Berkeley, Dept Phys, Berkeley, CA 94720 USA
[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
来源
PHYSICA D | 1999年 / 132卷 / 03期
基金
美国国家科学基金会;
关键词
Turing instability; Brusselator and Lengyel-Epstein models; three-dimensional patterns;
D O I
10.1016/S0167-2789(99)00041-X
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Existing group theoretic analysis of pattern formation in three dimensions [T.K. Callahan, E. Knobloch, Symmetry-breaking bifurcations on cubic lattices, Nonlinearity 10 (1997) 1179-1216] is used to make specific predictions about the formation of three-dimensional patterns in two models of the Turing instability. the Brusselator model and the Lengyel-Epstein model. Spatially periodic patterns having the periodicity of the simple cubic (SC), face-centered cubic (FCC) or body-centered cubic (BCC) lattices are considered. An efficient center manifold reduction is described and used to identify parameter regimes permitting stable lamella, SC, FCC, double-diamond, hexagonal prism. BCC and BCCI states. Both models possess a special wavenumber k(*) at which the normal form coefficients take on fixed model independent ratios and both are described by identical bifurcation diagrams. This property is generic for two-species chemical reaction-diffusion models with a single activator and inhibitor (C) 1999 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:339 / 362
页数:24
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