Dynamics of stochastic delay Lotka-Volterra systems with impulsive toxicant input and Lévy noise in polluted environments

In this paper, two stochastic delay Lotka-Volterra systems (i.e., competition system and predator-prey system) with impulsive toxicant input and Lévy noise in polluted environments are proposed and investigated. Under some simple assumptions, sufficient and necessary criteria for stability in time average and extinction of each population are established. The thresholds between stability in time average and extinction of each model are obtained. Some recent results are improved and extended greatly.