Mode transitions in a model reaction-diffusion system driven by domain growth and noise
Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction–diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences...
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| Format: | Journal article |
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2006
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| _version_ | 1797083314881822720 |
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| author | Barrass, I Crampin, E Maini, P |
| author_facet | Barrass, I Crampin, E Maini, P |
| author_sort | Barrass, I |
| collection | OXFORD |
| description | Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction–diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns. |
| first_indexed | 2024-03-07T01:40:00Z |
| format | Journal article |
| id | oxford-uuid:9689107d-f23c-4952-91e3-97bf12290845 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:40:00Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:9689107d-f23c-4952-91e3-97bf122908452022-03-26T23:53:32ZMode transitions in a model reaction-diffusion system driven by domain growth and noiseJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9689107d-f23c-4952-91e3-97bf12290845Mathematical Institute - ePrints2006Barrass, ICrampin, EMaini, PPattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction–diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns. |
| spellingShingle | Barrass, I Crampin, E Maini, P Mode transitions in a model reaction-diffusion system driven by domain growth and noise |
| title | Mode transitions in a model reaction-diffusion system driven by domain growth and noise |
| title_full | Mode transitions in a model reaction-diffusion system driven by domain growth and noise |
| title_fullStr | Mode transitions in a model reaction-diffusion system driven by domain growth and noise |
| title_full_unstemmed | Mode transitions in a model reaction-diffusion system driven by domain growth and noise |
| title_short | Mode transitions in a model reaction-diffusion system driven by domain growth and noise |
| title_sort | mode transitions in a model reaction diffusion system driven by domain growth and noise |
| work_keys_str_mv | AT barrassi modetransitionsinamodelreactiondiffusionsystemdrivenbydomaingrowthandnoise AT crampine modetransitionsinamodelreactiondiffusionsystemdrivenbydomaingrowthandnoise AT mainip modetransitionsinamodelreactiondiffusionsystemdrivenbydomaingrowthandnoise |