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Optimal harvesting of a stochastic mutualism model with Lévy jumps

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  • Liu, Meng
  • Bai, Chuanzhi

Abstract

In this letter, a stochastic mutualism model with Lévy jumps and harvesting is considered. Under some simple assumptions, sufficient and necessary criteria for the existence of optimal harvesting policy are established. The optimal harvesting effort and the maximum of sustainable yield are also obtained. The effects of random noises on the optimal harvesting of the model are discussed and some numerical simulations are introduced to illustrate the main results.

Suggested Citation

  • Liu, Meng & Bai, Chuanzhi, 2016. "Optimal harvesting of a stochastic mutualism model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 301-309.
    • Handle: RePEc:eee:apmaco:v:276:y:2016:i:c:p:301-309
    DOI: 10.1016/j.amc.2015.11.089
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    References listed on IDEAS

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    1. Kunita, Hiroshi, 2010. "Itô's stochastic calculus: Its surprising power for applications," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 622-652, May.
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    Cited by:

    1. Jeong, Yong Dam & Kim, Sangil & Jung, Il Hyo & Cho, Giphil, 2021. "Optimal harvesting strategy for hairtail, Trichiurus Lepturus, in Korea Sea using discrete-time age-structured model," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    2. Liu, Meng & Bai, Chuanzhi, 2020. "Optimal harvesting of a stochastic mutualism model with regime-switching," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    3. 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.
    4. Sheng Wang & Linshan Wang & Tengda Wei, 2018. "Optimal Harvesting for a Stochastic Predator-prey Model with S-type Distributed Time Delays," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 37-68, March.
    5. 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).
    6. Pal, D. & Samanta, G.P. & Mahapatra, G.S., 2017. "Selective harvesting of two competing fish species in the presence of toxicity with time delay," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 74-93.
    7. Wu, Jian, 2020. "Dynamics of a two-predator one-prey stochastic delay model with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    8. Zhang, Xiao-Bing & Chang, Suqin & Shi, Qihong & Huo, Hai-Feng, 2018. "Qualitative study of a stochastic SIS epidemic model with vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 805-817.
    9. 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.
    10. Zhang, Yan & Chen, Shihua & Gao, Shujing & Wei, Xiang, 2017. "Stochastic periodic solution for a perturbed non-autonomous predator–prey model with generalized nonlinear harvesting and impulses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 347-366.

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