Titre :

Equilibrium and surviving species in a large Lotka–Volterra system of differential equations

Auteur(s) :

Clenet, Maxime [Auteur]
Massol, Francois [Auteur]
Centre d’Infection et d’Immunité de Lille - INSERM U 1019 - UMR 9017 - UMR 8204 [CIIL]
Najim, Jamal [Auteur]

Titre de la revue :

Journal of Mathematical Biology

Pagination :

13

Éditeur :

Springer

Date de publication :

2023-07

ISSN :

0303-6812

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

Lotka-Volterra (LV) equations play a key role in the mathematical modeling of various ecological, biological and chemical systems. When the number of species (or, depending on the viewpoint, chemical components) becomes ...
Lire la suite >Lotka-Volterra (LV) equations play a key role in the mathematical modeling of various ecological, biological and chemical systems. When the number of species (or, depending on the viewpoint, chemical components) becomes large, basic but fundamental questions such as computing the number of surviving species still lack theoretical answers. In this paper, we consider a large system of LV equations where the interactions between the various species are a realization of a random matrix. We provide conditions to have a unique equilibrium and present a heuristics to compute the number of surviving species. This heuristics combines arguments from Random Matrix Theory, mathematical optimization (LCP), and standard extreme value theory. Numerical simulations, together with an empirical study where the strength of interactions evolves with time, illustrate the accuracy and scope of the results.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Centre d'Infection et d'Immunité de Lille (CIIL) - U1019 - UMR 9017

Source :

Harvested from HAL