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

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 show...

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G. C. Cruywagen More by this author
P. K. Maini More by this author
J. D. Murray More by this author
Publication date:
1997
URN:
uuid:f6717eda-4784-4c29-99df-b46a2c26b4a0
Local pid:
oai:eprints.maths.ox.ac.uk:457

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