Stability and Extinction for Lotka–Volterra Systems with Infinite Delay

Abstract

The paper deals with the global stability of a saturated equilibrium $${x^{\ast} = (x_1^{\ast}, \ldots, x_n^{\ast}) \ge 0}$$ for a multi-species Lotka–Volterra model with infinite delay. We assume the existence of non-delayed diagonal intraspecific competition terms, but relax the usual conditions of dominance which permit to control the infinite delay effect. Our results also apply to non-autonomous Lotka–Volterra systems without saturated equilibria, by studying the stability of their limiting equations. Some known results in the literature are improved and generalized.