Models to Assess the Effects of Nonsmooth Control and Stochastic Perturbation on Pest Control: A Pest-Natural-Enemy Ecosystem

Abstract

This paper investigates the impact of the threshold control strategy and environmental randomness on pest control. Firstly, a fixed-time impulsive stochastic ecosystem with IPM strategy is proposed, where the local and global existence of positive solution and the boundedness of expectation are discussed in detail. Moreover a sufficient condition for the extinction of the pest population with probability-1 is given. Then, a state-dependent stochastic ecosystem with IPM strategy is proposed. By employing the numerical simulations, the effects of ambient noise intensity on pest-outbreak are discussed. The result shows that there is a close relationship among the frequency of pest-outbreak, ET, the environmental perturbation intensity, and control measures. This study helps us to understand the impact of random factors on pest-outbreak frequency by theoretical derivations and numerical simulations; the results have directive significance in the design of an optimal control strategy for the department of ecological agriculture.