Abstract
This article is concerned with the optimal harvesting of a predator–prey model with a prey refuge and imprecise biological parameters. We consider the model under impreciseness and introduce a parametric functional form of an interval which differs from those of models with precise biological parameters. The existence of all possible equilibria and stability of system are discussed. The bionomic equilibrium of the model is analyzed. Also, the optimal harvesting policy is derived using Pontryagin’s maximal principle. Numerical simulations are presented to verify the feasibilities of our analytical results.
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Acknowledgments
We would like to thank the referees for their careful reading of the original manuscript and their valuable comments and suggestions that greatly improved the presentation of this paper. The work is supported by the National Natural Science Foundation of China (Nos. 11261017, 11371161) and the State Foundation for Studying Abroad. The authors thank Professor Binxiang Dai for his many valuable ideas and discussions. Also, the authors are grateful to Professor Yiping Chen and Doctor Changcheng Xiang for their help in numerical simulations.
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Communicated by Geraldo Diniz.
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Wang, Q., Liu, Z., Zhang, X. et al. Incorporating prey refuge into a predator–prey system with imprecise parameter estimates. Comp. Appl. Math. 36, 1067–1084 (2017). https://doi.org/10.1007/s40314-015-0282-8
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DOI: https://doi.org/10.1007/s40314-015-0282-8