Modeling and analysis of a non-autonomous single-species model with impulsive and random perturbations

• A non-autonomous single-species model with impulsive and random perturbations is established.
• Asymptotic behaviors of system are discussed.
• Effects of impulsive and random perturbations on the asymptotic behaviors of system are investigated.

In this paper, we study the dynamic behaviors of a non-autonomous single-species model subject to impulsive and random perturbations. We first investigate the existence and uniqueness of the globally positive solution of the model. Secondly, a good understanding of the extinction, non-persistence in the mean, weak persistence, persistence in the mean and stochastic permanence of the model is obtained. Thirdly, we further examine the asymptotic pathwise estimation. Fourthly, it is shown that the model is globally attractive under some appropriate conditions. Finally, numerical simulations are presented to justify the analytical results.