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