The Mathematical Institute, University of Oxford, Eprints Archive

Turing pattern outside of the Turing domain

Flach, E. H. and Schnell, S. and Norbury, John (2006) Turing pattern outside of the Turing domain. Applied Mathematics Letters . (In Press)

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Abstract

There are two simple solutions to reaction-diffusion systems with limit-cycle reaction kinetics, producing oscillatory behaviour. The reaction parameter $\mu$ gives rise to a ‘space-invariant’ solution, and $\mu$ versus the ratio of the diffusion coefficients gives rise to a ‘time-invariant’ solution. We consider the case where both solution types may be possible. This leads to a refinement of the Turing model of pattern formation. We add convection to the system and investigate its effect. More complex solutions arise that appear to combine the two simple solutions. The convective system sheds light on the underlying behaviour of the diffusive system.

Item Type:Article
Subjects:D - G > Dynamical systems and ergodic theory
O - Z > Ordinary differential equations
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:278
Deposited By:Gareth Wyn Jones
Deposited On:02 Oct 2006
Last Modified:20 Jul 2009 14:19

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