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Uncertain Gordon-Schaefer model driven by Liu process

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  • Chen, Dan
  • Liu, Yang

Abstract

The purpose of this paper is to employ an uncertain differential equation to model the fish population. Assume that the dynamic noises are described by Liu process. This paper obtains an uncertain Gordon-Schaefer equation. Then the existence, uniqueness, inverse uncertainty distribution, and stability of the solution of the uncertain Gordon-Schaefer equation are discussed. Next, three applications of the solution are given. Furthermore, the moment estimation is applied to inferring the unknown parameters of the uncertain Gordon-Schaefer model, and a brief study of the halibut population is proposed. Finally, a paradox of the stochastic Gordon-Schaefer model is deduced.

Suggested Citation

  • Chen, Dan & Liu, Yang, 2023. "Uncertain Gordon-Schaefer model driven by Liu process," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    • Handle: RePEc:eee:apmaco:v:450:y:2023:i:c:s0096300323001807
    DOI: 10.1016/j.amc.2023.128011
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    References listed on IDEAS

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    1. Yang, Xiangfeng & Ralescu, Dan A., 2015. "Adams method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 993-1003.
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    4. Xiaowei Chen & Jing Li & Chen Xiao & Peilin Yang, 2021. "Numerical solution and parameter estimation for uncertain SIR model with application to COVID-19," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 189-208, June.
    5. Waichon Lio & Baoding Liu, 2021. "Initial value estimation of uncertain differential equations and zero-day of COVID-19 spread in China," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 177-188, June.
    6. 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.
    7. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    8. Liu, Z. & Yang, Y., 2021. "Uncertain pharmacokinetic model based on uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    9. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    10. Mohring, Herbert & Schroeter, John, 1991. "The Costs of Inefficient Fishery Regulation: A Partial Study of Pacific Halibut," ISU General Staff Papers 199106010700001228, Iowa State University, Department of Economics.
    11. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62, pages 124-124.
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    13. Tang, Han & Yang, Xiangfeng, 2021. "Uncertain chemical reaction equation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
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