Generalized logistic equation on Networks

Bilel Elbetch

doi:10.5802/crmath.460

Systèmes dynamiques

Generalized logistic equation on Networks

Bilel Elbetch ¹

¹ Department of Mathematics, University Dr. Moulay Tahar of Saida, Algeria

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 911-934.

Résumé

In this paper, we consider a general single species model in a heterogeneous environment of $n$ patches ( $n \geq 2$ ), where each patch follows a generalized logistic law. First, we prove the global stability of the model. Second, in the case of perfect mixing, i.e. when the migration rate tends to infinity, the total population follows a generalized logistic law with a carrying capacity which in general is different from the sum of the $n$ carrying capacities. Next, we give some properties of the total equilibrium population and we compute its derivative at no dispersal. 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. Finally, we study an example of two-patch model where the first patch follows a logistic law and the second a Richard’s law, we give a complete classification of the model parameter space as to whether dispersal is beneficial or detrimental to the sum of two carrying capacities.

Reçu le : 2022-11-11
Révisé le : 2022-12-20
Accepté le : 2022-12-24
Publié le : 2023-07-18

DOI : 10.5802/crmath.460

Classification : 37N25, 92D25, 34D23, 34D15

Affiliations des auteurs :

Bilel Elbetch ¹

¹ Department of Mathematics, University Dr. Moulay Tahar of Saida, Algeria

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Bilel Elbetch},
     title = {Generalized logistic equation on {Networks}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {911--934},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.460},
     language = {en},
}

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Bilel Elbetch. Generalized logistic equation on Networks. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 911-934. doi : 10.5802/crmath.460. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.460/

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