

Preprint 64/2004
The effect of growth and curvature on pattern formation
Ramón G. Plaza, Faustino Sanchez-Garduno, Pablo Padilla, Rafael A. Barrio, and Philip K. Maini
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Submission date: 28. Sep. 2004 (revised version: October 2004)
Pages: 25
published in: Journal of dynamics and differential equations, 16 (2004) 4, p. 1093-1121
DOI number (of the published article): 10.1007/s10884-004-7834-8
Bibtex
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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 . 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.