This article is cited in 2 papers

METHODOLOGICAL NOTES

Turing patterns and Newell – Whitehead – Segel amplitude equation

E. P. Zemskov

Department of Continuum Mechanics, Dorodnitsyn Computing Centre, Russian Academy of Sciences

Abstract: Two-dimensional (2D) reaction–diffusion type systems with linear and nonlinear diffusion terms are examined for their behavior when a Turing instability emerges and stationary spatial patterns form. It is shown that a 2D nonlinear analysis for striped patterns leads to the Newell – Whitehead – Segel amplitude equation in which the contribution from spatial derivatives depends only on the linearized diffusion term of the original model. In the absence of this contribution, i.e., for the normal forms, standard methods are used to calculate the coefficients of the equation.

Keywords: Reaction-diffusion systems, Turing instability, amplitude equations.

PACS: 05.45.-a, 47.54.-r, 82.40.Bj, 82.40.Ck

Received: December 25, 2013
Revised: February 11, 2014
Accepted: February 11, 2014

DOI: 10.3367/UFNr.0184.201410j.1149

 English version: Physics–Uspekhi, 2014, 57:10, 1035–1037

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