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EQUILIBRIUM IN A LARGE LOTKA-VOLTERRA SYSTEM WITH PAIRWISE CORRELATED INTERACTIONS

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.
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https://hal.archives-ouvertes.fr/hal-03681747
Contributor : Jamal Najim Connect in order to contact the contributor
Submitted on : Monday, May 30, 2022 - 3:09:09 PM
Last modification on : Thursday, June 23, 2022 - 6:22:41 AM

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  • HAL Id : hal-03681747, version 1
  • ARXIV : 2205.15591

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Maxime Clenet, E Ferchichi, Jamal Najim. EQUILIBRIUM IN A LARGE LOTKA-VOLTERRA SYSTEM WITH PAIRWISE CORRELATED INTERACTIONS. 2022. ⟨hal-03681747⟩

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