title: Analysis of stationary droplets in a generic Turing reaction-diffusion system.
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, 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.
authors.affiliation: Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, United Kingdom. woolley@maths.ox.ac.uk
authors.forename: Thomas E
authors.initials: TE
authors.lastname: Woolley
authors.forename: Ruth E
authors.initials: RE
authors.lastname: Baker
authors.forename: Philip K
authors.initials: PK
authors.lastname: Maini
authors.forename: José Luis
authors.initials: JL
authors.lastname: Aragón
authors.forename: Rafael A
authors.initials: RA
authors.lastname: Barrio
mesh_terms: D004058:Diffusion; D008954:Models, Biological; D013269:Stochastic Processes