THE MULTI-PATCH LOGISTIC EQUATION

Bilel Elbetch (1) , Tounsia Benzekri (2) , Daniel Massart (3) , Tewfik Sari (4)

1 Université de Saïda Dr Moulay Tahar
2 USTHB - Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger]
3 IMAG - Institut Montpelliérain Alexander Grothendieck
4 UMR ITAP - Information – Technologies – Analyse Environnementale – Procédés Agricoles

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.

Domaines: Systèmes dynamiques [math.DS]

Bilel Elbetch, Tounsia Benzekri, Daniel Massart, Tewfik Sari. THE MULTI-PATCH LOGISTIC EQUATION. 2020. ⟨hal-02906124v1⟩