A Nonlinear Analysis of a Mechanical Model for Biological Pattern Formation
- 1 October 1988
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Mathematics
- Vol. 48 (5) , 1064-1072
- https://doi.org/10.1137/0148062
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 discussedKeywords
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