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Optimal harvesting of a stochastic delay competitive Lotka–Volterra model with Lévy jumps

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  • Qiu, Hong
  • Deng, Wenmin

Abstract

This paper systematically investigates the optimal harvesting of a stochastic delay competitive Lotka–Volterra model with Lévy jumps. Under some simple assumptions, the sufficient conditions for extinction and stable in the time average of each species are established. The stability in distribution of this model is proved under our assumptions. Finally, the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are also obtained. And some numerical simulations are introduced to demonstrate the theoretical results.

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  • 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.
    • Handle: RePEc:eee:apmaco:v:317:y:2018:i:c:p:210-222
    DOI: 10.1016/j.amc.2017.08.044
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    References listed on IDEAS

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    1. Liu, Meng & Bai, Chuanzhi, 2016. "Dynamics of a stochastic one-prey two-predator model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 308-321.
    2. Liu, Jiamin & Wei, Fengying, 2016. "Dynamics of stochastic SEIS epidemic model with varying population size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 241-250.
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    Cited by:

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    2. 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.
    3. Rong Liu & Guirong Liu, 2018. "Asymptotic Behavior of a Stochastic Two-Species Competition Model under the Effect of Disease," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    4. Liu, Meng & Bai, Chuanzhi, 2020. "Optimal harvesting of a stochastic mutualism model with regime-switching," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    5. Liu, Meng & Yu, Jingyi & Mandal, Partha Sarathi, 2018. "Dynamics of a stochastic delay competitive model with harvesting and Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 335-349.
    6. 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).
    7. Jang, Geunsoo & Cho, Giphil, 2022. "Optimal harvest strategy based on a discrete age-structured model with monthly fishing effort for chub mackerel, Scomber japonicus, in South Korea," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    8. Liu, Chao & Wang, Luping & Zhang, Qingling & Li, Yuanke, 2018. "Modeling and dynamical analysis of a triple delayed prey–predator–scavenger system with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1216-1239.

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