STABILITY OF A STOCHASTIC DISCRETE PREDATOR-PREY MODEL WITH TWO DELAYS

. This paper is concerned with the stability of a class of stochastic discrete predator-prey models with time delay. Based on a continuous predatorprey model with stochastic noise disturbance, a stochastic discrete model is obtained by using the Euler-Maruyama method. When the fear response time delay tau 1 and gestation time delay tau 2 are constant delays or varying delays, we obtain sufficient conditions for the stability in probability of the stochastic discrete system at the equilibrium point by using Lyapunov function. Finally, the conclusions are verified through numerical simulations.