Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation
The aim of the present review is to provide a comprehensive explanation of Turing reaction–diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction–diffusion model is widely studied in the field of mathematical biology, serves as a powerful p...
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| Format: | Journal article |
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2004
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| _version_ | 1826295943348092928 |
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| author | Miura, T Maini, P |
| author_facet | Miura, T Maini, P |
| author_sort | Miura, T |
| collection | OXFORD |
| description | The aim of the present review is to provide a comprehensive explanation of Turing reaction–diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction–diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for self-organization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction–diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology. |
| first_indexed | 2024-03-07T04:08:44Z |
| format | Journal article |
| id | oxford-uuid:c718a726-fc10-4ecb-acb6-8bf4ab289d69 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:08:44Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:c718a726-fc10-4ecb-acb6-8bf4ab289d692022-03-27T06:42:38ZPeriodic pattern formation in reaction-diffusion systems -an introduction for numerical simulationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c718a726-fc10-4ecb-acb6-8bf4ab289d69Mathematical Institute - ePrints2004Miura, TMaini, PThe aim of the present review is to provide a comprehensive explanation of Turing reaction–diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction–diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for self-organization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction–diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology. |
| spellingShingle | Miura, T Maini, P Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation |
| title | Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation |
| title_full | Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation |
| title_fullStr | Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation |
| title_full_unstemmed | Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation |
| title_short | Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation |
| title_sort | periodic pattern formation in reaction diffusion systems an introduction for numerical simulation |
| work_keys_str_mv | AT miurat periodicpatternformationinreactiondiffusionsystemsanintroductionfornumericalsimulation AT mainip periodicpatternformationinreactiondiffusionsystemsanintroductionfornumericalsimulation |