Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation |
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| Authors: | P K Maini M R Myerscough K H Winter J D Murray |
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| Institution: | (1) Department of Mathematics, University of Utah, 84112 Salt Lake City, UT, USA;(2) School of Mathematics and Statistics, University of Sydney, 2006 Sydney, N.S.W., Australia;(3) Theoretical Studies Department, Harwell Laboratory, 11 ORA Didcot, OX, UK;(4) Applied Mathematics, University of Washington, 98195 Seattle, WA, USA;(5) Present address: Centre for Mathematical Biology, Mathematical Institute, 24-29 St. Giles’, 3LB Oxford, OX1, UK |
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| 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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