Open AccessThe multi-patch logistic equation with asymmetric migration
Author(s) -
Bilel Elbetch,
Tounsia Benzekri,
Daniel Massart,
Tewfik Sari
Publication year - 2022
Publication title -
integración/revista integración, temas de matemáticas
Language(s) - English
Resource type - Journals
eISSN - 2145-8472
pISSN - 0120-419X
DOI - 10.18273/revint.v40n1-2022002
Subject(s) - carrying capacity , logistic function , population , mathematics , work (physics) , statistical physics , infinity , drop (telecommunication) , fragmentation (computing) , mathematical analysis , physics , statistics , thermodynamics , computer science , demography , biology , ecology , telecommunications , sociology , operating system
This paper is a follow-up to a previous work where we considered a multi-patch model, each patch following a logistic law, the patches being coupled by symmetric migration terms. In this paper we drop the symmetry hypothesis. First, 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, 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.