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Dynamical analysis and optimal control in a hybrid stochastic double delayed bioeconomic system with impulsive contaminants emission and Lévy jumps

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  • Liu, Chao
  • Xun, Xinying
  • Zhang, Qingling
  • Li, Yuanke

Abstract

In this paper, a hybrid stochastic double delayed prey predator bioeconomic system with impulses and Lévy jumps is established, where commercial harvesting on each population and impulsive contaminants emission from surrounding environment on each population growth are taken into account. Sufficient conditions for persistence in the mean and extinction of interacting population are investigated. The asymptotical stability in distribution of the proposed system is studied. Furthermore, optimal price control strategy and maximum of expectation of sustainable yield are discussed. Numerical simulations are carried out to illustrate theoretical analysis.

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  • Liu, Chao & Xun, Xinying & Zhang, Qingling & Li, Yuanke, 2019. "Dynamical analysis and optimal control in a hybrid stochastic double delayed bioeconomic system with impulsive contaminants emission and Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 99-118.
    • Handle: RePEc:eee:apmaco:v:352:y:2019:i:c:p:99-118
    DOI: 10.1016/j.amc.2019.01.045
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    1. Xinyou Meng & Qingling Zhang, 2015. "Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-15, October.
    2. Liu, Meng & Bai, Chuanzhi & Deng, Meiling & Du, Bo, 2016. "Analysis of stochastic two-prey one-predator model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 176-188.
    3. Zhou, Yanli & Yuan, Sanling & Zhao, Dianli, 2016. "Threshold behavior of a stochastic SIS model with Le´vy jumps," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 255-267.
    4. Yu, Jingyi & Liu, Meng, 2017. "Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 14-28.
    5. Zhang, Yue & Zhang, Qingling & Yan, Xing-Gang, 2014. "Complex dynamics in a singular Leslie–Gower predator–prey bioeconomic model with time delay and stochastic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 180-191.
    6. Zhang, Yue & Zheng, Yan & Liu, Xi & Zhang, Qingling & Li, Aihua, 2016. "Dynamical analysis of a differential algebraic bio-economic model with stage-structured and stochastic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 222-229.
    7. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 9, pages 178-203, Palgrave Macmillan.
    8. Yang, Xiaofeng & Jin, Zhen & Xue, Yakui, 2007. "Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 726-735.
    9. Qiu, Hong & Deng, Wenmin, 2018. "Optimal harvesting of a stochastic delay competitive Lotka–Volterra model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 210-222.
    10. Liu, Chao & Wang, Luping & Zhang, Qingling & Yan, Yun, 2017. "Dynamical analysis in a bioeconomic phytoplankton zooplankton system with double time delays and environmental stochasticity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 682-698.
    11. Liu, Chao & Yu, Longfei & Zhang, Qingling & Li, Yuanke, 2018. "Dynamic analysis of a hybrid bioeconomic plankton system with double time delays and stochastic fluctuations," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 115-137.
    12. Liu, Lidan & Meng, Xinzhu & Zhang, Tonghua, 2017. "Optimal control strategy for an impulsive stochastic competition system with time delays and jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 99-113.
    13. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62(2), pages 124-124.
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    Cited by:

    1. Liu, Chao & Xun, Xinying & Zhang, Guilai & Li, Yuanke, 2020. "Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

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