Kar, T. K.; Pahari, U. K.; Chaudhuri, K. S. Management of a prey-predator fishery based on continuous fishing effort. (English) Zbl 1124.91355 J. Biol. Syst. 12, No. 3, 301-313 (2004). Summary: This paper deals with the problem of selective harvesting in a hybrid type of prey-predator model. Here we have taken the fishing effort as a dynamic variable and tax as a control instrument. The existence of the possible steady states along with their local stability is discussed. The optimal tax policy is also discussed with the help of Pontryagin’s maximum principle. Finally, two numerical examples are taken to illustrate some of the key results. Cited in 8 Documents MSC: 91B76 Environmental economics (natural resource models, harvesting, pollution, etc.) 49N90 Applications of optimal control and differential games Keywords:selective harvesting; hybrid type of prey-predator model; Holling-Tanner; dynamic variable; optimal tax policy PDFBibTeX XMLCite \textit{T. K. Kar} et al., J. Biol. Syst. 12, No. 3, 301--313 (2004; Zbl 1124.91355) Full Text: DOI References: [1] DOI: 10.2307/1241552 · doi:10.2307/1241552 [2] DOI: 10.1016/0304-3800(86)90091-8 · doi:10.1016/0304-3800(86)90091-8 [3] DOI: 10.1016/0304-3800(88)90041-5 · doi:10.1016/0304-3800(88)90041-5 [4] Clark C. W., The Optimal Management of Renewable Resources: Mathematical Bio-economics (1990) · Zbl 0712.90018 [5] Clark C. W., Bioeconomic Modelling and Fisheries Management (1985) [6] DOI: 10.1142/S0218339002000494 · Zbl 1109.92313 · doi:10.1142/S0218339002000494 [7] DOI: 10.1142/S0218339003000725 · Zbl 1072.91033 · doi:10.1142/S0218339003000725 [8] DOI: 10.1016/0304-3800(94)00079-W · doi:10.1016/0304-3800(94)00079-W [9] Holling C. S., Mem. Entomol. Soc. Can. 45 pp 1– [10] DOI: 10.1080/00207390210131533 · Zbl 02348616 · doi:10.1080/00207390210131533 [11] DOI: 10.1142/S0218339003000828 · Zbl 1074.91035 · doi:10.1142/S0218339003000828 [12] DOI: 10.1080/0020739031000078730 · Zbl 02353962 · doi:10.1080/0020739031000078730 [13] DOI: 10.1006/bulm.1997.0023 · Zbl 1053.92521 · doi:10.1006/bulm.1997.0023 [14] May R. M., Stability and Complexity in Model Ecosystems (1974) [15] Pontryagin L. S., The Mathematical Theory of Optimal Processes (1964) [16] DOI: 10.2307/3146156 · doi:10.2307/3146156 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.