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 |
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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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