Stochastic IPM: Discrete Crop‐Pest‐Natural Enemy Dynamics With Environmental Noise

ABSTRACT In this paper, based on Euler–Marryama method and the theory of stochastic processes, considering that changes in crop, pest and natural enemy populations can be affected by environmental white noise during the process of integrated pest management (IPM), the data of biological samples is usually collected in discrete time, and the successive generations of many species in nature are nonoverlapping, a stochastic discrete crop‐pest‐natural enemy model is established and investigated. Firstly, the stability of the equilibria of deterministic continuous crop‐pest‐natural enemy model with IPM strategy is analyzed. Secondly, by using Lyapunov function and the theory of stochastic difference equation, sufficient conditions for the asymptotic mean square stability of the linearized stochastic difference equation corresponding to its translational transformation at zero solution are given, thus the stability in probability of the nonlinear stochastic discrete crop‐pest‐natural enemy model at the pest‐extinction equilibrium and positive equilibrium are obtained. Further, numerical simulations are used to confirm the theoretical results. Finally, considering that white noise mainly affects the growth rate and mortality rate of crop, pest and natural enemy populations, an improved stochastic discrete crop‐pest‐natural enemy model is established to investigate the effects of white noise intensity on population survival, and the results show that weak‐intensity noise dose not affect the survival and extinction of the population, however, high‐intensity noise may cause extinction in previously persistent populations.