Perumpanani, A. J. and Sherratt, J. A. and Maini, P. K. (1995) Phase differences in reactiondiffusionadvection systems and applications to morphogenesis. IMA Journal of Applied Mathematics, 55 (1). pp. 1933.

PDF
617kB 
Abstract
The authors study the effect of advection on reactiondiffusion patterns. It is shown that the addition of advection to a twovariable 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 Turingtype 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:  29 May 2015 18:22 
Repository Staff Only: item control page