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Article Dans Une Revue Revista Integración, temas de matemáticas Année : 2022

The multi-patch logistic equation with asymmetric migration

Résumé

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.
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Dates et versions

hal-03179136 , version 1 (24-03-2021)
hal-03179136 , version 2 (17-05-2021)
hal-03179136 , version 3 (18-05-2021)
hal-03179136 , version 4 (15-01-2022)

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Citer

Bilel Elbetch, Tounsia Benzekri, Daniel Massart, Tewfik Sari. The multi-patch logistic equation with asymmetric migration. Revista Integración, temas de matemáticas, 2022, 40 (1), pp.25-57. ⟨10.18273/revint.v40n1-2022002⟩. ⟨hal-03179136v4⟩
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