Analysis of stationary droplets in a generic Turing reaction-diffusion system
Por:
Woolley T.E., Baker R.E., Maini P.K., Aragón J.L., Barrio R.A.
Publicada:
23 nov 2010
Resumen:
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.
Filiaciones:
Woolley T.E.:
Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom
Baker R.E.:
Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom
Maini P.K.:
Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom
Oxford Centre for Integrative Systems Biology, Department of Biochemistry, University of Oxford, South Parks Road, Oxford OX1 3QU, United Kingdom
Aragón J.L.:
UNAM, Ctr Fis Aplicada & Tecnol Avanzada, Queretaro 76000, Mexico
Barrio R.A.:
Univ Nacl Autonoma Mexico, Inst Fis, Mexico City 01000, DF, Mexico
All Open Access; Green
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