The Mathematical Institute, University of Oxford, Eprints Archive

Biological pattern formation on two-dimensional domains: A nonlinear bifurcation analysis

Cruywagen, G. C. and Maini, P. K. and Murray, J. D. (1997) Biological pattern formation on two-dimensional domains: A nonlinear bifurcation analysis. SIAM Journal of Applied Mathematics, 57 (6). pp. 1485-1509.

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Abstract

A tissue interaction model for skin organ pattern formation is presented. Possible spatially patterned solutions on rectangular domains are investigated. Linear stability analysis suggests that the model can exhibit pattern formation. A weakly nonlinear two-dimensional perturbation analysis is then carried out. This demonstrates that when bifurcation occurs via a simple eigenvalue, patterns such as rolls, squares, and rhombi can be supported by the model equations. Our nonlinear analysis shows that more complex patterns are also possible if bifurcation occurs via a double eigenvalue. Surprisingly, hexagonal patterns could not develop from a primary bifurcation.

Item Type:Article
Uncontrolled Keywords:pattern formation; nonlinear bifurcation analyses; tissue interaction
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:457
Deposited By:Philip Maini
Deposited On:06 Dec 2006
Last Modified:20 Jul 2009 14:21

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