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Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern formation

Abstract:
We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989,J. exp. Zool. 251, 186–202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting patterns. We also investigate in-depth bifurcating solutions as the chemotactic parameter varies. This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns.

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P. K. Maini More by this author
M. R. Myerscough More by this author
J. D. Murray More by this author
K. H. Winters More by this author
Publication date:
1991
URN:
uuid:960c50c1-3548-4b2a-834c-754107410d40
Local pid:
oai:eprints.maths.ox.ac.uk:559

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