The Mathematical Institute, University of Oxford, Eprints Archive

The effect of growth and curvature on pattern formation

Plaza, R. and Sánchez-Garduño, F. and Padilla, P. and Barrio, R. A. and Maini, P. K. (2004) The effect of growth and curvature on pattern formation. Journal of Dynamics and Differential Equations, 16 (4). pp. 1093-1121.

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Abstract

Abstract Based on first principles, we derive a general model to describe the spatio-temporal dynamics of two morphogens. The diffusive part of the model incorporates the dynamics, growth and curvature of one- and two-dimensional domains embedded in 3. Our generalized diffusion process includes spatio-temporal varying diffusion coefficients, advection, and dilution terms. We present specific examples by analyzing a third order activator--inhibitor mechanism for the kinetic part. We carry out illustrative numerical simulations on two-dimensional growing domains having different geometries. Comparisons with former results on fixed domains show the crucial role of growth and curvature of pattern selection. Evidence is given that both effects might be biologically relevant in explaining the selection of some observed patterns and in changing or enhancing their stability.

Item Type:Article
Uncontrolled Keywords:Pattern formation - curvature - growth - reaction–diffusion
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:353
Deposited By:Philip Maini
Deposited On:10 Nov 2006
Last Modified:20 Jul 2009 14:20

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