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Complex dynamics and optimal harvesting strategy of competitive harvesting models with interval-valued imprecise parameters

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  • Tian, Yuan
  • Li, Chunxue
  • Liu, Jing

Abstract

Considering that species in nature are affected by the complexity of the ecosystem, biological parameters present certain inaccuracy or uncertainty. Different species exhibit different living habits, so it is of certain interest to investigate species related imprecise parameters. Besides, from the perspective of scientific and reasonable exploitation and utilization of fishery resources, two types of two-species competitive models with species related interval-valued imprecise parameters and harvesting are established. Firstly, the influence of interval-valued imprecise parameters on the dynamic behavior of the system without harvest are analyzed. Then, for continuous harvesting system, the existence of bio-economic equilibrium is discussed, and the optimal harvesting strategy is obtained by using Pontryagin’s maximum principle. Next, for the system guided by weighted harvesting strategy, the existence and stability of the order-1 periodic solution are discussed. Besides, in order to find the harvesting strategy that maximizes the economic profit in the harvest process, an optimization problem is constructed according to the actual situation, and the optimal set values of the weight and threshold of the strategy are obtained. Finally, the correctness of the obtained results and the feasibility of the harvesting strategy are verified through numerical simulation in MATLAB. The results of this study provide a reference for the scientific and reasonable exploitation and utilization of competitive fishery resources in the imprecise parameter environment.

Suggested Citation

  • Tian, Yuan & Li, Chunxue & Liu, Jing, 2023. "Complex dynamics and optimal harvesting strategy of competitive harvesting models with interval-valued imprecise parameters," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922012632
    DOI: 10.1016/j.chaos.2022.113084
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    1. Guo, Hongjian & Chen, Lansun & Song, Xinyu, 2015. "Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 905-922.
    2. Wenbo Zhao & Caochuan Ma & Lijun Chen, 2014. "Multiple Periodic Solutions of an Impulsive Population System with Delays," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, May.
    3. Jiang, Guirong & Lu, Qishao & Qian, Linning, 2007. "Complex dynamics of a Holling type II prey–predator system with state feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 448-461.
    4. Song, Xinyu & Li, Yongfeng, 2007. "Dynamic complexities of a Holling II two-prey one-predator system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 463-478.
    5. Zhang, Tongqian & Ma, Wanbiao & Meng, Xinzhu & Zhang, Tonghua, 2015. "Periodic solution of a prey–predator model with nonlinear state feedback control," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 95-107.
    6. Zhao, Yu & Yuan, Sanling, 2017. "Optimal harvesting policy of a stochastic two-species competitive model with Lévy noise in a polluted environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 20-33.
    7. Saed Mallak & Doa’a Farekh & Basem Attili, 2021. "Numerical Investigation of Fuzzy Predator-Prey Model with a Functional Response of the Form Arctan ( ax )," Mathematics, MDPI, vol. 9(16), pages 1-22, August.
    8. Li, Wenjie & Huang, Lihong & Guo, Zhenyuan & Ji, Jinchen, 2020. "Global dynamic behavior of a plant disease model with ratio dependent impulsive control strategy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 120-139.
    9. Castillo-Alvino, Hamlet Humberto & Marvá, Marcos, 2022. "Group defense promotes coexistence in interference competition: The Holling type IV competitive response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 426-445.
    10. Tian, Yuan & Gao, Yan & Sun, Kaibiao, 2022. "Global dynamics analysis of instantaneous harvest fishery model guided by weighted escapement strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    11. Tian, Yuan & Sun, Kaibiao & Chen, Lansun, 2011. "Modelling and qualitative analysis of a predator–prey system with state-dependent impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 318-331.
    12. Anjana Das & M. Pal, 2019. "Theoretical Analysis of an Imprecise Prey-Predator Model with Harvesting and Optimal Control," Journal of Optimization, Hindawi, vol. 2019, pages 1-12, January.
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