Stability analysis of a stochastic discrete pest-natural enemy model with integrated pest management strategy

The successive generations of many species in nature are non-overlapping, and the data of biological samples is usually collected in discrete time, so using discrete-time models can better describe population changes. Pest control is an important part of agricultural production safety and ecological environment protection, but the process will be affected by environmental white noise. On the one hand, fluctuations in temperature can lead to variations in the density of pest and natural enemy populations. On the other hand, the effects of pesticides to pests are also influenced by white noise. Based on these, a stochastic discrete pest-natural enemy model with white noise and integrated pest management is established. Firstly, we discuss the stability of the equilibria of its corresponding deterministic discrete pest-natural enemy model. Secondly, based on the criterion of asymptotically mean-square stability of the zero solution of the general linear stochastic discrete model, sufficient conditions are obtained for the equilibria of the stochastic discrete pest-natural enemy model to be stable in probability. Then the numerical simulations are used to confirm the applications of the theoretical results and to discuss the effects of important parameters on the extinction of pest population. Finally, considering that white noise mainly affects the growth rate and mortality rate of pest and natural enemy populations, an improved stochastic discrete pest-natural enemy model is established, and we discuss the effects of the perturbation intensity of white noise on the persistence and extinction of population.