Management of a prey-predator fishery based on continuous fishing effort. (English) Zbl 1124.91355

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.


91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
49N90 Applications of optimal control and differential games
Full Text: DOI


[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 · doi:10.1080/00207390210131533
[11] DOI: 10.1142/S0218339003000828 · Zbl 1074.91035 · doi:10.1142/S0218339003000828
[12] DOI: 10.1080/0020739031000078730 · 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
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