The Mathematical Institute, University of Oxford, Eprints Archive

Pattern formation in generalised Turing systems: I. Steady-state patterns in systems with mixed boundary conditions

Dillon, R. and Maini, P. K. and Othmer, H. G. (1994) Pattern formation in generalised Turing systems: I. Steady-state patterns in systems with mixed boundary conditions. Journal of Mathematical Biology, 32 (4). pp. 345-393.

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Abstract

Turing's model of pattern formation has been extensively studied analytically and numerically, and there is recent experimental evidence that it may apply in certain chemical systems. The model is based on the assumption that all reacting species obey the same type of boundary condition pointwise on the boundary. We call these scalar boundary conditions. Here we study mixed or nonscalar boundary conditions, under which different species satisfy different boundary conditions at any point on the boundary, and show that qualitatively new phenomena arise in this case. For example, we show that there may be multiple solutions at arbitrarily small lengths under mixed boundary conditions, whereas the solution is unique under homogeneous scalar boundary conditions. Moreover, even when the same solution exists under scalar and mixed boundary conditions, its stability may be different in the two cases. We also show that mixed boundary conditions can reduce the sensitivity of patterns to domain changes.

Item Type:Article
Uncontrolled Keywords:Spatial pattern formations - Bifurcation - Turing systems
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:500
Deposited By:Philip Maini
Deposited On:12 Dec 2006
Last Modified:20 Jul 2009 14:21

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