Parameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearity
new type of instability in coupled reaction-diffusion-advection systems is analysed in a one-dimensional domain. This instability, arising due to the combined action of flow and diffusion, creates spatially periodic stationary waves termed flow and diffusion-distributed structures (FDS). Here we sho...
| Main Authors: | , , |
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| Format: | Journal article |
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2001
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| _version_ | 1797054934890315776 |
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| author | Satnoianu, R Maini, P Menzinger, M |
| author_facet | Satnoianu, R Maini, P Menzinger, M |
| author_sort | Satnoianu, R |
| collection | OXFORD |
| description | new type of instability in coupled reaction-diffusion-advection systems is analysed in a one-dimensional domain. This instability, arising due to the combined action of flow and diffusion, creates spatially periodic stationary waves termed flow and diffusion-distributed structures (FDS). Here we show, via linear stability analysis, that FDS are predicted in a considerably wider domain and are more robust (in the parameter domain) than the classical Turing instability patterns. FDS also represent a natural extension of the recently discovered flow-distributed oscillations (FDO). Nonlinear bifurcation analysis and numerical simulations in one-dimensional spatial domains show that FDS also have much richer solution behaviour than Turing structures. In the framework presented here Turing structures can be viewed as a particular instance of FDS. We conclude that FDS should be more easily obtainable in chemical systems than Turing (and FDO) structures and that they may play a potentially important role in biological pattern formation. |
| first_indexed | 2024-03-06T19:04:19Z |
| format | Journal article |
| id | oxford-uuid:149c9df1-07e2-4dfb-9d7a-222bd1f1a1bd |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:04:19Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:149c9df1-07e2-4dfb-9d7a-222bd1f1a1bd2022-03-26T10:20:45ZParameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:149c9df1-07e2-4dfb-9d7a-222bd1f1a1bdMathematical Institute - ePrints2001Satnoianu, RMaini, PMenzinger, Mnew type of instability in coupled reaction-diffusion-advection systems is analysed in a one-dimensional domain. This instability, arising due to the combined action of flow and diffusion, creates spatially periodic stationary waves termed flow and diffusion-distributed structures (FDS). Here we show, via linear stability analysis, that FDS are predicted in a considerably wider domain and are more robust (in the parameter domain) than the classical Turing instability patterns. FDS also represent a natural extension of the recently discovered flow-distributed oscillations (FDO). Nonlinear bifurcation analysis and numerical simulations in one-dimensional spatial domains show that FDS also have much richer solution behaviour than Turing structures. In the framework presented here Turing structures can be viewed as a particular instance of FDS. We conclude that FDS should be more easily obtainable in chemical systems than Turing (and FDO) structures and that they may play a potentially important role in biological pattern formation. |
| spellingShingle | Satnoianu, R Maini, P Menzinger, M Parameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearity |
| title | Parameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearity |
| title_full | Parameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearity |
| title_fullStr | Parameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearity |
| title_full_unstemmed | Parameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearity |
| title_short | Parameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearity |
| title_sort | parameter domains for turing and stationary flow distributed waves i the influence of nonlinearity |
| work_keys_str_mv | AT satnoianur parameterdomainsforturingandstationaryflowdistributedwavesitheinfluenceofnonlinearity AT mainip parameterdomainsforturingandstationaryflowdistributedwavesitheinfluenceofnonlinearity AT menzingerm parameterdomainsforturingandstationaryflowdistributedwavesitheinfluenceofnonlinearity |