Fuzzy optimal harvesting of a prey-predator model in the presence of toxicity with prey refuge under imprecise parameters

Shuqi Zhai; Qinglong Wang; Ting Yu; Shuqi Zhai; Qinglong Wang; Ting Yu

doi:10.3934/mbe.2022558

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 11983-12012. doi: 10.3934/mbe.2022558

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Research article

Fuzzy optimal harvesting of a prey-predator model in the presence of toxicity with prey refuge under imprecise parameters

School of Mathematics and Statistics, Hubei Minzu University, Enshi 445000, China

Academic Editor： Hao Wang

Received: 03 June 2022 Revised: 25 July 2022 Accepted: 07 August 2022 Published: 18 August 2022

The objective of this paper is to investigate the dynamic behaviors of a prey-predator model incorporating the effect of toxic substances with prey refuge under imprecise parameters. We handle these biological parameters in model by using interval numbers. The existence together with stability of biological equilibria are obtained. We also analyze the existence conditions of the bionomic equilibria. The optimal harvesting strategy is explored by taking into account instantaneous annual discount rate under fuzzy conditions. Three numeric examples are performed to illustrate our analytical findings.
- prey-predator model,
- imprecise parameter,
- refuge,
- toxicity,
- equilibria,
- stability,
- fuzzy optimal harvesting
Citation: Shuqi Zhai, Qinglong Wang, Ting Yu. Fuzzy optimal harvesting of a prey-predator model in the presence of toxicity with prey refuge under imprecise parameters[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 11983-12012. doi: 10.3934/mbe.2022558

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Abstract

The objective of this paper is to investigate the dynamic behaviors of a prey-predator model incorporating the effect of toxic substances with prey refuge under imprecise parameters. We handle these biological parameters in model by using interval numbers. The existence together with stability of biological equilibria are obtained. We also analyze the existence conditions of the bionomic equilibria. The optimal harvesting strategy is explored by taking into account instantaneous annual discount rate under fuzzy conditions. Three numeric examples are performed to illustrate our analytical findings.

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