A nonlinear analysis of a mechanical model for pattern formation
This paper studies a simplified but biologically relevant version of a mechanical model for morphogenesis proposed by Oster, Murray, and Harris [J. Embryol. Exp. Morph., 78 (1983), pp. 83–125]. A nonlinear bifurcation analysis of the partial differential system is presented. In the one-dimensional v...
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| Format: | Journal article |
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1988
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| _version_ | 1826267843131342848 |
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| author | Maini, P Murray, J |
| author_facet | Maini, P Murray, J |
| author_sort | Maini, P |
| collection | OXFORD |
| description | This paper studies a simplified but biologically relevant version of a mechanical model for morphogenesis proposed by Oster, Murray, and Harris [J. Embryol. Exp. Morph., 78 (1983), pp. 83–125]. A nonlinear bifurcation analysis of the partial differential system is presented. In the one-dimensional version, the derivation of the amplitude equation involves a nonstandard element. The analysis of a caricature of the two-dimensional system predicts the formation of rolls and hexagons. The biological significance of these results to feather germ formation is briefly discussed. |
| first_indexed | 2024-03-06T21:00:26Z |
| format | Journal article |
| id | oxford-uuid:3ab49be8-28cb-47b9-9e32-6beb77e76ab2 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:00:26Z |
| publishDate | 1988 |
| record_format | dspace |
| spelling | oxford-uuid:3ab49be8-28cb-47b9-9e32-6beb77e76ab22022-03-26T14:03:10ZA nonlinear analysis of a mechanical model for pattern formationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3ab49be8-28cb-47b9-9e32-6beb77e76ab2Mathematical Institute - ePrints1988Maini, PMurray, JThis paper studies a simplified but biologically relevant version of a mechanical model for morphogenesis proposed by Oster, Murray, and Harris [J. Embryol. Exp. Morph., 78 (1983), pp. 83–125]. A nonlinear bifurcation analysis of the partial differential system is presented. In the one-dimensional version, the derivation of the amplitude equation involves a nonstandard element. The analysis of a caricature of the two-dimensional system predicts the formation of rolls and hexagons. The biological significance of these results to feather germ formation is briefly discussed. |
| spellingShingle | Maini, P Murray, J A nonlinear analysis of a mechanical model for pattern formation |
| title | A nonlinear analysis of a mechanical model for pattern formation |
| title_full | A nonlinear analysis of a mechanical model for pattern formation |
| title_fullStr | A nonlinear analysis of a mechanical model for pattern formation |
| title_full_unstemmed | A nonlinear analysis of a mechanical model for pattern formation |
| title_short | A nonlinear analysis of a mechanical model for pattern formation |
| title_sort | nonlinear analysis of a mechanical model for pattern formation |
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