Dynamics of a stochastic Holling II one-predator two-prey system with jumps

In this paper, a stochastic Holling II one-predator two-prey system with jumps is investigated. Firstly, the properties of the solution, such as the existence and uniqueness of the global positive solution, stochastic ultimate boundedness and the pathwise estimation are studied. Then we mainly establish the sufficient conditions for the extinction and persistence in the mean of the solution. Results show that positive jump noise is advantageous to the system while negative jump noise is disadvantageous. Finally, a numerical example is introduced to illustrate the results.