Dynamics of a stochastic population model with Allee effect and jumps

Abstract

This paper is concerned with a stochastic population model with Allee effect and jumps. First, we show the global existence of almost surely positive solution to the model. Next, exponential extinction and persistence in mean are discussed. Then, we investigated the global attractivity and stability in distribution. At last, some numerical results are given. The results show that if attack rate $a$ is in the intermediate range or very large, the population will go extinct. Under the premise that attack rate $a$ is less than growth rate $r$, if the noise intensity or jump is relatively large, the population will become extinct; on the contrary, the population will be persistent in mean. The results in this paper generalize and improve the previous related results.