Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients
Reaction-diffusion models for biological pattern formation have been studied extensively in a variety of embryonic and ecological contexts. However, despite experimental evidence pointing to the existence of spatial inhomogeneities in various biological systems, most models have only been considered...
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| Format: | Journal article |
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1992
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| _version_ | 1797097435449786368 |
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| author | Maini, P Benson, D Sherratt, J |
| author_facet | Maini, P Benson, D Sherratt, J |
| author_sort | Maini, P |
| collection | OXFORD |
| description | Reaction-diffusion models for biological pattern formation have been studied extensively in a variety of embryonic and ecological contexts. However, despite experimental evidence pointing to the existence of spatial inhomogeneities in various biological systems, most models have only been considered in a spatially homogeneous environment. The authors consider a two-chemical reaction-diffusion mechanism in one space dimension in which one of the diffusion coefficients depends explicitly on the spatial variable. The model is analysed in the case of a step function diffusion coefficient and the insight gained for this special case is used to discuss pattern generation for smoothly varying diffusion coefficients. The results show that spatial inhomogeneity may be an important biological pattern regulator, and possible applications of the model to chondrogenesis in the vertebrate limb are suggested. |
| first_indexed | 2024-03-07T04:55:28Z |
| format | Journal article |
| id | oxford-uuid:d674ebea-9067-43c1-afed-efa0c4f2bd67 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:55:28Z |
| publishDate | 1992 |
| record_format | dspace |
| spelling | oxford-uuid:d674ebea-9067-43c1-afed-efa0c4f2bd672022-03-27T08:33:35ZPattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficientsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d674ebea-9067-43c1-afed-efa0c4f2bd67Mathematical Institute - ePrints1992Maini, PBenson, DSherratt, JReaction-diffusion models for biological pattern formation have been studied extensively in a variety of embryonic and ecological contexts. However, despite experimental evidence pointing to the existence of spatial inhomogeneities in various biological systems, most models have only been considered in a spatially homogeneous environment. The authors consider a two-chemical reaction-diffusion mechanism in one space dimension in which one of the diffusion coefficients depends explicitly on the spatial variable. The model is analysed in the case of a step function diffusion coefficient and the insight gained for this special case is used to discuss pattern generation for smoothly varying diffusion coefficients. The results show that spatial inhomogeneity may be an important biological pattern regulator, and possible applications of the model to chondrogenesis in the vertebrate limb are suggested. |
| spellingShingle | Maini, P Benson, D Sherratt, J Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| title | Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| title_full | Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| title_fullStr | Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| title_full_unstemmed | Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| title_short | Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| title_sort | pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| work_keys_str_mv | AT mainip patternformationinreactiondiffusionmodelswithspatiallyinhomogeneousdiffusioncoefficients AT bensond patternformationinreactiondiffusionmodelswithspatiallyinhomogeneousdiffusioncoefficients AT sherrattj patternformationinreactiondiffusionmodelswithspatiallyinhomogeneousdiffusioncoefficients |