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...
| Principais autores: | , , , , |
|---|---|
| Formato: | Journal article |
| Publicado em: |
American Physical Society
2012
|
| _version_ | 1826281655926521856 |
|---|---|
| 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 | 2024-03-07T00:32:04Z |
| format | Journal article |
| id | oxford-uuid:8025fcc2-1df4-41f2-8d61-c366b39095ae |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:32:04Z |
| publishDate | 2012 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:8025fcc2-1df4-41f2-8d61-c366b39095ae2022-03-26T21:21:30ZNonlinear effects on Turing patterns: time oscillations and chaosJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8025fcc2-1df4-41f2-8d61-c366b39095aeMathematical Institute - ePrintsAmerican Physical Society2012Aragón, 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 |
| work_keys_str_mv | AT aragonj nonlineareffectsonturingpatternstimeoscillationsandchaos AT barrior nonlineareffectsonturingpatternstimeoscillationsandchaos AT woolleyt nonlineareffectsonturingpatternstimeoscillationsandchaos AT bakerr nonlineareffectsonturingpatternstimeoscillationsandchaos AT mainip nonlineareffectsonturingpatternstimeoscillationsandchaos |