Author(s)

Xuegui Zhang, Yuanfu Shao^*, Taolin Zhang

College of Science, Guilin University of Technology, Guilin, China.

In this paper, the dynamics of a stochastic ratio-dependent predator-prey system with markovian switching and Lévy noise is studied. Firstly, we show the existence condition of global positive solution under the given positive initial value. Secondly, sufficient conditions for system extinction and persistence are obtained through some assumptions. Then, the sufficient conditions of stochastically persistence are obtained by combining stochastic analysis technique and M-matrix analysis. In addition, under appropriate conditions, we demonstrate the existence of a unique stationary distribution for a system without Lévy jumps. Finally, the empirical and Mlistein methods are used to verify the theoretical results through numerical simulation.

Ratio-Dependent Predator-Prey System, Lévy, Stochastically Permanence, Ergodicity

Zhang, X. , Shao, Y. and Zhang, T. (2020) Analysis of a Stochastic Ratio-Dependent Predator-Prey System with Markovian Switching and Lévy Jumps. Journal of Applied Mathematics and Physics, 8, 2632-2657. doi: 10.4236/jamp.2020.811195.