Nonlinear effects on Turing patterns: time oscillations and chaos.
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...
| Auteurs principaux: | , , , , |
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| Format: | Journal article |
| Langue: | English |
| Publié: |
2012
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| _version_ | 1826273727797526528 |
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| author | Aragón, J Barrio, R Woolley, T Baker, R Maini, P |
| author_facet | Aragón, J Barrio, R Woolley, T Baker, R Maini, P |
| author_sort | Aragón, J |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T22:32:37Z |
| format | Journal article |
| id | oxford-uuid:58c6a9da-fe52-4c91-89a4-11dbb2c37831 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:32:37Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:58c6a9da-fe52-4c91-89a4-11dbb2c378312022-03-26T17:05:42ZNonlinear effects on Turing patterns: time oscillations and chaos.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:58c6a9da-fe52-4c91-89a4-11dbb2c37831EnglishSymplectic Elements at Oxford2012Aragón, JBarrio, RWoolley, TBaker, RMaini, PWe 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. |
| spellingShingle | Aragón, J Barrio, R Woolley, T Baker, R Maini, P Nonlinear effects on Turing patterns: time oscillations and chaos. |
| title | Nonlinear effects on Turing patterns: time oscillations and chaos. |
| title_full | Nonlinear effects on Turing patterns: time oscillations and chaos. |
| title_fullStr | Nonlinear effects on Turing patterns: time oscillations and chaos. |
| title_full_unstemmed | Nonlinear effects on Turing patterns: time oscillations and chaos. |
| title_short | Nonlinear effects on Turing patterns: time oscillations and chaos. |
| title_sort | nonlinear effects on turing patterns time oscillations and chaos |
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