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Two-patch herbivore/vegetation models with density-dependent migration
In this thesis we constructed two mathematical models for herbivore/vegetation interactions in environment of two patches, using the metaphysiological approach and a density-dependent migrations. In the first model we considered the case when the environment is constant, and we constructed a system...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2018
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| _version_ | 1867613190901202944 |
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| access_status_str | Open Access |
| author | Bakheet, Mohamed Abdalaziz Abdalla |
| author2 | Laurie, Henri |
| author_browse | Bakheet, Mohamed Abdalaziz Abdalla Laurie, Henri |
| author_facet | Laurie, Henri Bakheet, Mohamed Abdalaziz Abdalla |
| author_sort | Bakheet, Mohamed Abdalaziz Abdalla |
| collection | Thesis |
| dc_rights_str_mv | Creative Commons Attribution 4.0 International (CC BY 4.0) http://creativecommons.org/licenses/by/4.0/ |
| description | In this thesis we constructed two mathematical models for herbivore/vegetation interactions in environment of two patches, using the metaphysiological approach and a density-dependent migrations. In the first model we considered the case when the environment is constant, and we constructed a system of four perturbed ordinary differential equations describing the dynamics when only herbivores allowed to move between the two patches searching for food. The model contain two different timescales, fast for migrations and slow for the other demographic changes in the system. We used the geometric singular perturbation theory in order to reduce the dimension of the system. Using the continuation software AUTO we provided bifurcation diagrams for the reduced systems and we also provided some numerical illustrations to show the dynamics of the system for different migrations propensities. We analyzed the bifurcation diagrams using Morse decompositions and Conley index theory, to confirm their correctness. We constructed a second mathematical model, by considering that the vegetation growth depends on seasonal rainfall and the soil moisture. We provided some numerical simulations to illustrate several variates of dynamics for different migration speed and, when the migration propensities and the vegetation quality are change. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/28921 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:13.078Z |
| license_str | Creative Commons |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2018 |
| publishDateRange | 2018 |
| publishDateSort | 2018 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/28921 Two-patch herbivore/vegetation models with density-dependent migration Bakheet, Mohamed Abdalaziz Abdalla Laurie, Henri In this thesis we constructed two mathematical models for herbivore/vegetation interactions in environment of two patches, using the metaphysiological approach and a density-dependent migrations. In the first model we considered the case when the environment is constant, and we constructed a system of four perturbed ordinary differential equations describing the dynamics when only herbivores allowed to move between the two patches searching for food. The model contain two different timescales, fast for migrations and slow for the other demographic changes in the system. We used the geometric singular perturbation theory in order to reduce the dimension of the system. Using the continuation software AUTO we provided bifurcation diagrams for the reduced systems and we also provided some numerical illustrations to show the dynamics of the system for different migrations propensities. We analyzed the bifurcation diagrams using Morse decompositions and Conley index theory, to confirm their correctness. We constructed a second mathematical model, by considering that the vegetation growth depends on seasonal rainfall and the soil moisture. We provided some numerical simulations to illustrate several variates of dynamics for different migration speed and, when the migration propensities and the vegetation quality are change. 2018-10-10T08:52:16Z 2018-10-10T08:52:16Z 2013 Master Thesis Masters PhD http://hdl.handle.net/11427/28921 eng Creative Commons Attribution 4.0 International (CC BY 4.0) http://creativecommons.org/licenses/by/4.0/ application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Bakheet, Mohamed Abdalaziz Abdalla Two-patch herbivore/vegetation models with density-dependent migration |
| thesis_degree_str | Doctoral |
| title | Two-patch herbivore/vegetation models with density-dependent migration |
| title_full | Two-patch herbivore/vegetation models with density-dependent migration |
| title_fullStr | Two-patch herbivore/vegetation models with density-dependent migration |
| title_full_unstemmed | Two-patch herbivore/vegetation models with density-dependent migration |
| title_short | Two-patch herbivore/vegetation models with density-dependent migration |
| title_sort | two patch herbivore vegetation models with density dependent migration |
| url | http://hdl.handle.net/11427/28921 |
| work_keys_str_mv | AT bakheetmohamedabdalazizabdalla twopatchherbivorevegetationmodelswithdensitydependentmigration |