Shoji H, Yamada K, Ueyama D, Ohta T. Turing patterns in three dimensions.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007;
75:046212. [PMID:
17500983 DOI:
10.1103/physreve.75.046212]
[Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2006] [Indexed: 05/15/2023]
Abstract
We investigate three-dimensional Turing patterns in two-component reaction diffusion systems. The FitzHugh-Nagumo equation, the Brusselator, and the Gray-Scott model are solved numerically in three dimensions. Several interconnected structures of domains as well as lamellar, hexagonal, and spherical domains are obtained as stable motionless equilibrium patterns. The relative stability of these structures is studied analytically based on the reduction approximation. The relation with the microphase-separated structures in block copolymers is also discussed.
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