The Mathematical Institute, University of Oxford, Eprints Archive

Nonlinear 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) Nonlinear effects on Turing patterns: time oscillations and chaos. Physical Review E, 86 (2). 026201-1. ISSN 1063-651X

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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, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1580
Deposited By:Philip Maini
Deposited On:11 Aug 2012 06:58
Last Modified:08 Oct 2012 13:54

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