The Mathematical Institute, University of Oxford, Eprints Archive

Phase differences in reaction-diffusion-advection systems and applications to morphogenesis

Perumpanani, A. J. and Sherratt, J. A. and Maini, P. K. (1995) Phase differences in reaction-diffusion-advection systems and applications to morphogenesis. IMA Journal of Applied Mathematics, 55 (1). pp. 19-33.

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Abstract

The authors study the effect of advection on reaction-diffusion patterns. It is shown that the addition of advection to a two-variable reaction–diffusion system with periodic boundary conditions results in the appearance of a phase difference between the patterns of the two variables which depends on the difference between the advection coefficients. The spatial patterns move like a travelling wave with a fixed velocity which depends on the sum of the advection coefficients. By a suitable choice of advection coefficients, the solution can be made stationary in time. In the presence of advection a continuous change in the diffusion coefficients can result in two Turing-type bifurcations as the diffusion ratio is varied, and such a bifurcation can occur even when the inhibitor species does not diffuse. It is also shown that the initial mode of bifurcation for a given domain size depends on both the advection and diffusion coefficients. These phenomena are demonstrated in the numerical solution of a particular reaction–diffusion system, and finally a possible application of the results to pattern formation in Drosophila larvae is discussed.

Item Type:Article
Uncontrolled Keywords:n/a
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:477
Deposited By:Philip Maini
Deposited On:10 Dec 2006
Last Modified:20 Jul 2009 14:21

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