The multi-patch logistic equation with asymmetric migration
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917594297008128 |
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| author | Elbetch, Bilel Benzekri, Tounsia Massart, Daniel Sari, Tewfik |
| author_facet | Elbetch, Bilel Benzekri, Tounsia Massart, Daniel Sari, Tewfik |
| contents | This paper considers a multi-patch model, where each patch follows a logistic law, and patches are coupled by asymmetrical migration terms. First, in the case of perfect mixing, i.e when the migration rate tends to infinity, the total population follows a logistic equation with a carrying capacity which in general is different from the sum of the n carrying capacities, and depends on the migration terms. Second, we determine, in some particular cases, the conditions under which fragmentation and asymmetrical migration can lead to a total equilibrium population greater or smaller than the sum of the carrying capacities. Finally, for the three-patch model, we show numerically the existence of at least three critical values of the migration rate for which the total equilibrium population equals the sum of the carrying capacities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_13144 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The multi-patch logistic equation with asymmetric migration Elbetch, Bilel Benzekri, Tounsia Massart, Daniel Sari, Tewfik Dynamical Systems 37N25, 92D25 This paper considers a multi-patch model, where each patch follows a logistic law, and patches are coupled by asymmetrical migration terms. First, in the case of perfect mixing, i.e when the migration rate tends to infinity, the total population follows a logistic equation with a carrying capacity which in general is different from the sum of the n carrying capacities, and depends on the migration terms. Second, we determine, in some particular cases, the conditions under which fragmentation and asymmetrical migration can lead to a total equilibrium population greater or smaller than the sum of the carrying capacities. Finally, for the three-patch model, we show numerically the existence of at least three critical values of the migration rate for which the total equilibrium population equals the sum of the carrying capacities. |
| title | The multi-patch logistic equation with asymmetric migration |
| topic | Dynamical Systems 37N25, 92D25 |
| url | https://arxiv.org/abs/2103.13144 |