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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series B Année : 2021

The multi-Patch logistic equation

Résumé

The paper considers a n-patch model with migration terms, where each patch follows a logistic law. First, we give some properties of the total equilibrium population. In some particular cases, we determine the conditions under which fragmentation and migration can lead to a total equilibrium population which might be greater or smaller than the sum of the n carrying capacities. Second, in the case of perfect mixing, i.e when the migration rate tends to infinity, the total population follows a logistic law with a carrying capacity which in general is different from the sum of the n carrying capacities. Finally, for the three-patch model we show numerically that the increase in number of patches from two to three gives a new behavior for the dynamics of the total equilibrium population as a function of the migration rate.
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Dates et versions

hal-02906124 , version 1 (24-07-2020)
hal-02906124 , version 2 (16-01-2021)

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Bilel Elbetch, Tounsia Benzekri, Daniel Massart, Tewfik Sari. The multi-Patch logistic equation. Discrete and Continuous Dynamical Systems - Series B, 2021, 26 (12), pp.6405 - 6424. ⟨10.3934/dcdsb.2021025⟩. ⟨hal-02906124v2⟩
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