Deterministic and stochastic dynamics of a modified Leslie-Gower prey-predator system with simplified Holling-type Ⅳ scheme.

In this paper, a prey-predator model with modified Leslie-Gower and simplified Holling-type Ⅳ functional responses is proposed to study the dynamic behaviors. For the deterministic system, we analyze the permanence of the system and the stability of the positive equilibrium point. For the stochastic system, we not only prove the existence and uniqueness of global positive solution, but also discuss the persistence in mean and extinction of the populations. In addition, we find that stochastic system has an ergodic stationary distribution under some parameter constraints. Finally, our theoretical results are verified by numerical simulations.