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Dynamics of a stochastic delay competitive model with harvesting and Markovian switching

Author

Listed:
  • Liu, Meng
  • Yu, Jingyi
  • Mandal, Partha Sarathi

Abstract

This work is concerned with a two-species stochastic state-switching competitive population model with distributed delays and harvesting. First, necessary and sufficient criteria for the existence of a unique ergodic stationary distribution of the system are established. Then necessary and sufficient criteria for the existence of the optimal harvesting policy are given, and the explicit expression of the optimal harvesting policy is obtained. Finally, some effects of the state-switching on the persistence, extinction and optimal harvesting strategy of the system are discussed with the help of several simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:335-349
    DOI: 10.1016/j.amc.2018.03.044
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

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    2. Lan, Guijie & Wei, Chunjin & Zhang, Shuwen, 2019. "Long time behaviors of single-species population models with psychological effect and impulsive toxicant in polluted environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 828-842.
    3. Zhao, Xin & Zeng, Zhijun, 2020. "Stationary distribution and extinction of a stochastic ratio-dependent predator–prey system with stage structure for the predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Wang, Hui & Pan, Fangmei & Liu, Meng, 2019. "Survival analysis of a stochastic service–resource mutualism model in a polluted environment with pulse toxicant input," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 591-606.
    5. Liu, Yan & Zhang, Di & Su, Huan & Feng, Jiqiang, 2019. "Stationary distribution for stochastic coupled systems with regime switching and feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    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).

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