Nonlinear effects on Turing patterns: Time oscillations and chaos
Type
ArticleKAUST Grant Number
KUK-C1-013-04Date
2012-08-08Permanent link to this record
http://hdl.handle.net/10754/598988
Metadata
Show full item recordAbstract
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.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).Publisher
American Physical Society (APS)Journal
Physical Review EPubMed ID
23005839ae974a485f413a2113503eed53cd6c53
10.1103/PhysRevE.86.026201
Scopus Count
Collections
Publications Acknowledging KAUST SupportRelated articles
- Turing patterns beyond hexagons and stripes.
- Authors: Yang L, Dolnik M, Zhabotinsky AM, Epstein IR
- Issue date: 2006 Sep
- Noise-reversed stability of Turing patterns versus Hopf oscillations near codimension-two conditions.
- Authors: Alonso S, Sagués F
- Issue date: 2009 Sep
- Tunable oscillations and chaotic dynamics in systems with localized synthesis.
- Authors: Naqib F, Quail T, Musa L, Vulpe H, Nadeau J, Lei J, Glass L
- Issue date: 2012 Apr
- Control of spatiotemporal patterns in the Gray-Scott model.
- Authors: Kyrychko YN, Blyuss KB, Hogan SJ, Schöll E
- Issue date: 2009 Dec
- Multiple period-doubling bifurcation route to chaos in periodically pulsed Murali-Lakshmanan-Chua circuit-controlling and synchronization of chaos.
- Authors: Parthasarathy S, Manikandakumar K
- Issue date: 2007 Dec