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We study the equilibria of a large Lokta-Volterra system of coupleddifferential equations in the case where the interaction coefficients form alarge random matrix. In the case where this random matrix follows an ellipticmodel , we study the existence of a (componentwise) positive equilibrium anddescribe a phase transition for the matrix normalization.If there is nopositive equilibrium, we provide conditions on the model parameters for theexistence of a stable equilibrium (with vanishing components) and stateheuristics to compute the number of positive components of the equilibrium.Lotka-Volterra systems are important in mathematical biology/ theoreticalecology.

Equilibrium in a large Lotka-Volterra system with pairwise correlated interactions