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

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Abstract
We show that a model reactiondiffusion 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, quasiperiodic and chaotic oscillations without modifying the underlying Turing pattern. A RuelleTakensNewhouse 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 reactiondiffusion 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 08:11 
Last Modified:  29 May 2015 19:13 
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