Dynamics of a stochastic population model with Allee effect and Lévy jumps

Abstract

This article formulates and researches a single-species stochastic population model with Allee effect and Lévy jumps. Firstly, it is shown that the model has a unique global positive solution. Then sufficient conditions for extinction and stochastic permanence are obtained. Finally, the growth rate of the solution is estimated. The results demonstrate that the Lévy jumps could change the properties of the model significantly. Several numerical figures are given to explain the theoretical results.