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

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  • Xuewen Tan
  • Wenjie Qin
  • Guangyao Tang
  • Changcheng Xiang
  • Xinzhi Liu

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.

Suggested Citation

  • Xuewen Tan & Wenjie Qin & Guangyao Tang & Changcheng Xiang & Xinzhi Liu, 2019. "Models to Assess the Effects of Nonsmooth Control and Stochastic Perturbation on Pest Control: A Pest-Natural-Enemy Ecosystem," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    • Handle: RePEc:hin:complx:8326164
    DOI: 10.1155/2019/8326164
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    References listed on IDEAS

    as
    1. Obradović, Maja, 2019. "Implicit numerical methods for neutral stochastic differential equations with unbounded delay and Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 664-687.
    2. Peipei Wang & Wenjie Qin & Guangyao Tang, 2019. "Modelling and Analysis of a Host-Parasitoid Impulsive Ecosystem under Resource Limitation," Complexity, Hindawi, vol. 2019, pages 1-12, January.
    3. Zhang, Yan & Fan, Kuangang & Gao, Shujing & Liu, Yingfen & Chen, Shihua, 2019. "Ergodic stationary distribution of a stochastic SIRS epidemic model incorporating media coverage and saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 671-685.
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