Nonlinear effects on Turing patterns: Time oscillations and chaos
KAUST Grant NumberKUK-C1-013-04
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AbstractWe 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. © 2012 American Physical Society.
CitationAragón JL, Barrio RA, Woolley TE, Baker RE, Maini PK (2012) Nonlinear effects on Turing patterns: Time oscillations and chaos. Phys Rev E 86. Available: http://dx.doi.org/10.1103/PhysRevE.86.026201.
SponsorsThis work was supported by CONACyT and DGAPA-UNAM, Mexico, under Grants No. 79641 and No. IN100310-3, respectively, and was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
PublisherAmerican Physical Society (APS)
JournalPhysical Review E
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