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Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps

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  • Tingting Ma
  • Xinzhu Meng
  • Zhengbo Chang

Abstract

We consider a stochastic one-predator-two-prey harvesting model with time delays and Lévy jumps in this paper. Using the comparison theorem of stochastic differential equations and asymptotic approaches, sufficient conditions for persistence in mean and extinction of three species are derived. By analyzing the asymptotic invariant distribution, we study the variation of the persistent level of a population. Then we obtain the conditions of global attractivity and stability in distribution. Furthermore, making use of Hessian matrix method and optimal harvesting theory of differential equations, the explicit forms of optimal harvesting effort and maximum expectation of sustainable yield are obtained. Some numerical simulations are given to illustrate the theoretical results.

Suggested Citation

  • Tingting Ma & Xinzhu Meng & Zhengbo Chang, 2019. "Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps," Complexity, Hindawi, vol. 2019, pages 1-19, March.
    • Handle: RePEc:hin:complx:5342031
    DOI: 10.1155/2019/5342031
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    Cited by:

    1. Xiangrui Li & Shuibo Huang, 2019. "Stability and Bifurcation for a Single-Species Model with Delay Weak Kernel and Constant Rate Harvesting," Complexity, Hindawi, vol. 2019, pages 1-17, December.
    2. Dezhao Li & Huidong Cheng & Yu Liu, 2019. "Dynamic Analysis of Beddington–DeAngelis Predator-Prey System with Nonlinear Impulse Feedback Control," Complexity, Hindawi, vol. 2019, pages 1-13, November.
    3. Liu, Qun & Jiang, Daqing, 2020. "Threshold behavior in a stochastic SIR epidemic model with Logistic birth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. Liu, Guodong & Meng, Xinzhu, 2019. "Optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    5. Jinlei Liu & Wencai Zhao, 2019. "Dynamic Analysis of Stochastic Lotka–Volterra Predator-Prey Model with Discrete Delays and Feedback Control," Complexity, Hindawi, vol. 2019, pages 1-15, November.
    6. Jin, Xihua & Jia, Jianwen, 2020. "Qualitative study of a stochastic SIRS epidemic model with information intervention," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    7. Dongmei Yuan & Yuzhen Bai, 2019. "Stability of Traveling Wave Fronts for a Three Species Predator-Prey Model with Nonlocal Dispersals," Complexity, Hindawi, vol. 2019, pages 1-15, December.

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