The Mathematical Institute, University of Oxford, Eprints Archive

Analysis of stationary droplets in a generic Turing reaction-diffusion system

Woolley, T. E. and Baker, R. E. and Maini, P. K. and Aragón, J. L. and Barrio, R. A. (2010) Analysis of stationary droplets in a generic Turing reaction-diffusion system. Physical Review E, 82 (5). ISSN 1063-651X

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Abstract

Solitonlike structures called “droplets” are found to exist within a paradigm reaction-diffusion model that can be used to describe patterning in a number of biological systems, for example, on the skin of various fish species. They have also been found in many other systems that can be modeled with a complex Ginzburg-Landau system. These droplets can be analyzed in the biological paradigm model because the system has two nonzero stable steady states that are symmetric; however, the asymmetric case is more challenging. We first review the properties of the paradigm system and then extend a recently developed perturbation technique [D. Gomila et al., J. Opt. B: Quantum Semiclassical Opt. 6, S265 (2004)] to investigate the weakly asymmetric case. We compare the results of our mathematical analysis with numerical simulations and show good agreement in the region where the assumptions hold.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1022
Deposited By:Philip Maini
Deposited On:25 Nov 2010 07:56
Last Modified:08 Oct 2012 12:38

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