MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

The effect of growth and curvature on pattern formation

Ramón G. Plaza, Faustino Sanchez-Garduno, Pablo Padilla, Rafael A. Barrio and Philip K. Maini


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 ${\mathbb{R}}^{3}$. 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 on 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.


Related publications

2004 Repository Open Access
Ramon G. Plaza, Faustino Sanchez-Garduno, P. Padilla, R. A. Barrio and Philip K. Maini

The effect of growth and curvature on pattern formation

In: Journal of dynamics and differential equations, 16 (2004) 4, pp. 1093-1121