Asymptotic behavior of a non-autonomous predator-prey model with Hassell–Varley type functional response and random perturbation

Abstract

This paper considers a new non-autonomous predator-prey model with stochastic perturbation and Hassell–Varley type functional response. Based on classical comparison theorem of stochastic equations, $$It\hat{o}$$ ’s formula and skillful analysis techniques, the existence of a global positive solution and stochastically ultimate boundedness are derived. Furthermore, some sufficient and necessary criteria for extinction, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean and the global attractivity of the system are obtained. At last, a series of numerical simulations to illustrate our mathematical findings are presented and some conclusions are also given.