Nonlinear effects on Turing patterns: Time oscillations and chaos

Handle URI:
http://hdl.handle.net/10754/598988
Title:
Nonlinear effects on Turing patterns: Time oscillations and chaos
Authors:
Aragón, J. L.; Barrio, R. A.; Woolley, T. E.; Baker, R. E.; Maini, P. K.
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. © 2012 American Physical Society.
Citation:
Aragón 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.
Publisher:
American Physical Society (APS)
Journal:
Physical Review E
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
8-Aug-2012
DOI:
10.1103/PhysRevE.86.026201
PubMed ID:
23005839
Type:
Article
ISSN:
1539-3755; 1550-2376
Sponsors:
This 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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorAragón, J. L.en
dc.contributor.authorBarrio, R. A.en
dc.contributor.authorWoolley, T. E.en
dc.contributor.authorBaker, R. E.en
dc.contributor.authorMaini, P. K.en
dc.date.accessioned2016-02-25T13:50:41Zen
dc.date.available2016-02-25T13:50:41Zen
dc.date.issued2012-08-08en
dc.identifier.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.en
dc.identifier.issn1539-3755en
dc.identifier.issn1550-2376en
dc.identifier.pmid23005839en
dc.identifier.doi10.1103/PhysRevE.86.026201en
dc.identifier.urihttp://hdl.handle.net/10754/598988en
dc.description.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.en
dc.description.sponsorshipThis 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).en
dc.publisherAmerican Physical Society (APS)en
dc.titleNonlinear effects on Turing patterns: Time oscillations and chaosen
dc.typeArticleen
dc.identifier.journalPhysical Review Een
dc.contributor.institutionUniversidad Nacional Autonoma de Mexico, Mexico City, Mexicoen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en

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