Local and Global Stability for Lotka-Volterra Systems with Distributed Delays and Instantaneous Negative Feedbacks

This paper addresses the local and global stability of n-dimensional Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks. Necessary and sufficient conditions for local stability independent of the choice of the delay functions are given, by imposing a weak nondelayed diagonal dominance which cancels the delayed competition effect. The global asymptotic stability of positive equilibria is established under conditions slightly stronger than the ones required for the linear stability. For the case of monotone interactions, however, sharper conditions are presented. This paper generalizes known results for discrete delays to systems with distributed delays. Several applications illustrate the results. Keywords: Lotka-Volterra system, delayed population model, distributed delays, global asymptotic stability, local asymptotic stability, instantaneous negative feedback