Two impulsive stochastic delay single-species models incorporating Lévy noise

Two types of impulsive stochastic delay single-species models are proposed and investigated by taking Levy noise into account. Sufficient conditions for extinction are obtained as well as non-persistence in the mean, weak persistence and stochastic permanence. Numerical simulations carried out for resulting systems confirm our theoretical analysis results. The impacts of impulses, delays, white noises and Levy noise on the population dynamics are discussed.