Spatial and spatio-temporal patterns in a cell-haptotaxis model.
We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost th...
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| Format: | Journal article |
| Language: | English |
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Springer-Verlag
1989
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| _version_ | 1797068109949960192 |
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| author | Maini, P |
| author_facet | Maini, P |
| author_sort | Maini, P |
| collection | OXFORD |
| description | We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation. |
| first_indexed | 2024-03-06T22:05:57Z |
| format | Journal article |
| id | oxford-uuid:5024f387-0c74-4659-ab67-df33fb0ba437 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:05:57Z |
| publishDate | 1989 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | oxford-uuid:5024f387-0c74-4659-ab67-df33fb0ba4372022-03-26T16:11:51ZSpatial and spatio-temporal patterns in a cell-haptotaxis model.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:5024f387-0c74-4659-ab67-df33fb0ba437EnglishSymplectic Elements at OxfordSpringer-Verlag1989Maini, PWe investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation. |
| spellingShingle | Maini, P Spatial and spatio-temporal patterns in a cell-haptotaxis model. |
| title | Spatial and spatio-temporal patterns in a cell-haptotaxis model. |
| title_full | Spatial and spatio-temporal patterns in a cell-haptotaxis model. |
| title_fullStr | Spatial and spatio-temporal patterns in a cell-haptotaxis model. |
| title_full_unstemmed | Spatial and spatio-temporal patterns in a cell-haptotaxis model. |
| title_short | Spatial and spatio-temporal patterns in a cell-haptotaxis model. |
| title_sort | spatial and spatio temporal patterns in a cell haptotaxis model |
| work_keys_str_mv | AT mainip spatialandspatiotemporalpatternsinacellhaptotaxismodel |