Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern formation
We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989,J. exp. Zool. 251, 186–202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting pa...
| Main Authors: | , , , |
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| Format: | Journal article |
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1991
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| _version_ | 1797066280417624064 |
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| author | Maini, P Myerscough, M Murray, J Winters, K |
| author_facet | Maini, P Myerscough, M Murray, J Winters, K |
| author_sort | Maini, P |
| collection | OXFORD |
| description | We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989,J. exp. Zool. 251, 186–202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting patterns. We also investigate in-depth bifurcating solutions as the chemotactic parameter varies. This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns. |
| first_indexed | 2024-03-06T21:40:13Z |
| format | Journal article |
| id | oxford-uuid:47aaa8c5-38b6-4657-ab29-48c3238e649a |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:40:13Z |
| publishDate | 1991 |
| record_format | dspace |
| spelling | oxford-uuid:47aaa8c5-38b6-4657-ab29-48c3238e649a2022-03-26T15:21:19ZBifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern formationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:47aaa8c5-38b6-4657-ab29-48c3238e649aMathematical Institute - ePrints1991Maini, PMyerscough, MMurray, JWinters, KWe consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989,J. exp. Zool. 251, 186–202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting patterns. We also investigate in-depth bifurcating solutions as the chemotactic parameter varies. This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns. |
| spellingShingle | Maini, P Myerscough, M Murray, J Winters, K Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern formation |
| title | Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern formation |
| title_full | Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern formation |
| title_fullStr | Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern formation |
| title_full_unstemmed | Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern formation |
| title_short | Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern formation |
| title_sort | bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern formation |
| work_keys_str_mv | AT mainip bifurcatingspatiallyheterogeneoussolutionsinachemotaxismodelforbiologicalpatternformation AT myerscoughm bifurcatingspatiallyheterogeneoussolutionsinachemotaxismodelforbiologicalpatternformation AT murrayj bifurcatingspatiallyheterogeneoussolutionsinachemotaxismodelforbiologicalpatternformation AT wintersk bifurcatingspatiallyheterogeneoussolutionsinachemotaxismodelforbiologicalpatternformation |