Computer simulations of three-dimensional Turing patterns in the Lengyel-Epstein model

Hiroto Shoji and Takao Ohta
Phys. Rev. E 91, 032913 – Published 19 March 2015

Abstract

We investigate numerically Turing patterns in the Lengyel-Epstein model in three dimensions. In a bulk homogeneous system under periodic boundary conditions, we obtain not only lamellar, cylindrical, and spherical structures but also several interconnected periodic structures including the Schwartz P-surface structure. In order to examine Turing patterns in the conditions accessible experimentally, we consider inhomogeneous systems where a parameter in the reaction-diffusion equations depends on the space coordinate with either Dirichlet or Neumann boundary conditions. In this situation, we find that a perforated-lamellar structure and an Fddd structure, both of which have a uniaxial symmetry, appear depending on the boundary conditions.

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  • Received 7 January 2015

DOI:https://doi.org/10.1103/PhysRevE.91.032913

©2015 American Physical Society

Authors & Affiliations

Hiroto Shoji1 and Takao Ohta2,3

  • 1Department of Physics, Graduate School of Medical Science, Kyoto Prefectural University of Medicine, Taishogun, Kita-ku, Kyoto 603-8334, Japan
  • 2Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
  • 3Toyota Physical and Chemical Research Institute, Nagakute, Aichi 480-1192, Japan

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Vol. 91, Iss. 3 — March 2015

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