The Mathematical Institute, University of Oxford, Eprints Archive

Non-linear effects on Turing patterns: time oscillations and chaos.

Aragón, J. L. and Barrio, R. A. and Woolley, T. E. and Baker, R. E. and Maini, P. K. (2012) Non-linear effects on Turing patterns: time oscillations and chaos. Physical Review Letters . (Submitted)

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Abstract

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space, produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, Turing patterns oscillate in time, a phenomenon which is expected to occur only in a three morphogen system. When varying a single parameter, a series of bifurcations lead to period doubling, quasi-periodic and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examined the Turing conditions for obtaining a diffusion driven instability and discovered that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. All this results demonstrates the limitations of the linear analysis for reaction-diffusion systems.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1529
Deposited By:Peter Hudston
Deposited On:04 Jul 2012 09:11
Last Modified:08 Oct 2012 09:37

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