Qualitative analysis of a stochastic ratio-dependent Holling-Tanner system

This article addresses a stochastic ratio-dependent predator-prey system with Leslie-Gower and Holling type II schemes. Firstly, the existence of the global positive solution is shown by the comparison theorem of stochastic differential equations. Secondly, in the case of persistence, we prove that there exists a ergodic stationary distribution. Finally, numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings.