Dynamics of stochastic holling II predator-prey under Markovian-switching with jumps

Abstract

In this paper, a stochastic Holling II predator-prey model under Markovian switching with jumps is investigated. The aim is to find out how the Markovian switching and the jump noise affect the dynamics of this model. Firstly, we study the properties of the solutions, for example, the existence and uniqueness of the global positive solution, the uniform boundedness of the pth moment and the pathwise estimation. Secondly, sucient criteria for extinction and strong persistence in the mean are established. Results show that jump noise can essentially change the nature of the system, i.e., it can make strongly persistent species extinct and extinct species persistent. We also observe that both the overall extinction and strong persistence in the mean have close relationships with the stationary probability distribution of the Markov chain. Finally, numerical examples are introduced to illustrate the results.