Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients
We consider a reaction diffusion system in one spatial dimension in which the diffusion coefficients are spatially varying. We present a non-standard linear analysis for a certain class of spatially varying diffusion coefficients and show that it accurately predicts the behaviour of the full nonline...
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| Format: | Journal article |
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1993
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| _version_ | 1797061650436587520 |
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| author | Benson, D Maini, P Sherratt, J |
| author_facet | Benson, D Maini, P Sherratt, J |
| author_sort | Benson, D |
| collection | OXFORD |
| description | We consider a reaction diffusion system in one spatial dimension in which the diffusion coefficients are spatially varying. We present a non-standard linear analysis for a certain class of spatially varying diffusion coefficients and show that it accurately predicts the behaviour of the full nonlinear system near bifurcation. We show that the steady state solutions exhibit qualitatively different behaviour to that observed in the usual case with constant diffusion coefficients. Specifically, the modified system can generate patterns with spatially varying amplitude and wavelength. Application to chondrogenesis in the limb is discussed. |
| first_indexed | 2024-03-06T20:34:16Z |
| format | Journal article |
| id | oxford-uuid:3216f79f-fbc5-45e0-9b8c-c9d5c2be5a0f |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:34:16Z |
| publishDate | 1993 |
| record_format | dspace |
| spelling | oxford-uuid:3216f79f-fbc5-45e0-9b8c-c9d5c2be5a0f2022-03-26T13:11:51ZAnalysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficientsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3216f79f-fbc5-45e0-9b8c-c9d5c2be5a0fMathematical Institute - ePrints1993Benson, DMaini, PSherratt, JWe consider a reaction diffusion system in one spatial dimension in which the diffusion coefficients are spatially varying. We present a non-standard linear analysis for a certain class of spatially varying diffusion coefficients and show that it accurately predicts the behaviour of the full nonlinear system near bifurcation. We show that the steady state solutions exhibit qualitatively different behaviour to that observed in the usual case with constant diffusion coefficients. Specifically, the modified system can generate patterns with spatially varying amplitude and wavelength. Application to chondrogenesis in the limb is discussed. |
| spellingShingle | Benson, D Maini, P Sherratt, J Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| title | Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| title_full | Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| title_fullStr | Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| title_full_unstemmed | Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| title_short | Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| title_sort | analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients |
| work_keys_str_mv | AT bensond analysisofpatternformationinreactiondiffusionmodelswithspatiallyinhomogeneousdiffusioncoefficients AT mainip analysisofpatternformationinreactiondiffusionmodelswithspatiallyinhomogeneousdiffusioncoefficients AT sherrattj analysisofpatternformationinreactiondiffusionmodelswithspatiallyinhomogeneousdiffusioncoefficients |