The Mathematical Institute, University of Oxford, Eprints Archive

A nonlinear analysis of a mechanical model for pattern formation

Maini, P. K. and Murray, J. D. (1988) A nonlinear analysis of a mechanical model for pattern formation. SIAM Journal on Applied Mathematics, 48 (5). pp. 1064-1072.

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Abstract

This paper studies a simplified but biologically relevant version of a mechanical model for morphogenesis proposed by Oster, Murray, and Harris [J. Embryol. Exp. Morph., 78 (1983), pp. 83–125]. A nonlinear bifurcation analysis of the partial differential system is presented. In the one-dimensional version, the derivation of the amplitude equation involves a nonstandard element. The analysis of a caricature of the two-dimensional system predicts the formation of rolls and hexagons. The biological significance of these results to feather germ formation is briefly discussed.

Item Type:Article
Uncontrolled Keywords:biological pattern formation; bifurcation theory; mechanical models
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:530
Deposited By:Philip Maini
Deposited On:15 Dec 2006
Last Modified:20 Jul 2009 14:22

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