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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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Publication date:
1991-01-01
URN:
uuid:47aaa8c5-38b6-4657-ab29-48c3238e649a
Local pid:
oai:eprints.maths.ox.ac.uk:520

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