2022/05/31 by Maxime Clenet, Clenet, Maxime, E Ferchichi +3
Mathematics · Medicine · Social Sciences · #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.2205.15591
openalex publication_date 2022/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.