Equilibrium in a large Lotka-Volterra system with pairwise correlated interactions
Probability
2022-06-01 v1
Abstract
We study the equilibria of a large Lokta-Volterra system of coupled differential equations in the case where the interaction coefficients form a large random matrix. In the case where this random matrix follows an elliptic model , we study the existence of a (componentwise) positive equilibrium and describe a phase transition for the matrix normalization.If there is no positive equilibrium, we provide conditions on the model parameters for the existence of a stable equilibrium (with vanishing components) and state heuristics to compute the number of positive components of the equilibrium. Lotka-Volterra systems are important in mathematical biology/ theoretical ecology.
Keywords
Cite
@article{arxiv.2205.15591,
title = {Equilibrium in a large Lotka-Volterra system with pairwise correlated interactions},
author = {Maxime Clenet and E Ferchichi and Jamal Najim},
journal= {arXiv preprint arXiv:2205.15591},
year = {2022}
}