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\(N\)-species non-autonomous Lotka-Volterra competitive systems with delays and impulsive perturbations. (English) Zbl 1231.37055

Summary: A class of non-autonomous \(N\)-species Lotka-Volterra-type competitive system with time delays and impulsive perturbations is investigated. New criteria on coexistence and global attractivity for all species other than some inclining to extinction are established. From our results, we find that the extinction of some species due to competition exclusion and weak adaption to a stochastically variable environment characterized by impulsive perturbations is necessary for the coexistence and global attractivity of other survivors in a limited resource ecosystem. Meanwhile, the dynamic behaviors of competition models with impulse perturbations are more complicated and different from prior research results obtained from continuous competition models. The impulse perturbations impose either negative or positive influences on the survival of species, which results in evidently regulative effects, and even make the inferior competitors exclude or coexist with the superior competitors. The theoretical results are confirmed by a special example and numerical simulations, by which we find some interesting phenomena.

MSC:

37N25 Dynamical systems in biology
92D25 Population dynamics (general)
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