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

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 p...

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Bibliographic Details
Published in:Bulletin of mathematical biology 1991-09, Vol.53 (5), p.701-719
Main Authors: MAINI, P. K, MYERSCOUGH, M. R, WINTERS, K. H, MURRAY, J. D
Format: Article
Language:English
Subjects:
Animals
Biological and medical sciences
Cell Movement
Cell physiology
Chemotaxis
Embryonic and Fetal Development
Fundamental and applied biological sciences. Psychology
Models, Biological
Molecular and cellular biology
Motility and taxis
Skin Pigmentation
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Summary: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.
ISSN:0092-8240
1522-9602
DOI:10.1007/bf02461550