The Mathematical Institute, University of Oxford, Eprints Archive

Two dimensional pattern formation in a chemotactic system

Myerscough, M. R. and Maini, P. K. and Murray, J. D. and Winters, K. H. (1990) Two dimensional pattern formation in a chemotactic system. In: Dynamics of Complex Interconnected Biological Systems. n/a, n/a (n/a). Birkhauser, Boston, USA, pp. 65-83. ISBN n/a

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Abstract

Chemotaxis is known to be important in cell aggregation in a variety of contexts. We propose a simple partial differential equation model for a chemotactic system of two species, a population of cells and a chemoattractant to which cells respond. Linear analysis shows that there exists the possibility of spatially inhomogeneous solutions to the model equations for suitable choices of parameters.

We solve the full nonlinear steady state equations numerically on a two dimensional rectangular domain. By using mode selection from the linear analysis we produce simple pattern elements such as stripes and regular spots. More complex patterns evolve from these simple solutions as parameter values or domain shape change continuously. An example bifurcation diagram is calculated using the chemotactic response of the cells as the bifurcation parameter. These numerical solutions suggest that a chemotactic mechanism can produce a rich variety of complex patterns.

Item Type:Book Section
Uncontrolled Keywords:n/a
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:525
Deposited By:Philip Maini
Deposited On:15 Dec 2006
Last Modified:20 Jul 2009 14:22

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