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A predator-prey model for the optimal control of fish harvesting through the imposition of a tax.

Authors :
Chatterjee, Anal
Pal, Samares
Source :
International Journal of Optimization & Control: Theories & Applications; Jan2023, Vol. 13 Issue 1, p68-80, 13p
Publication Year :
2023

Abstract

This paper is devoted to the study of ecosystem based fisheries management. The model represents the interaction between prey and predator population with Holling II functional response consisting of different carrying capacities and constant intrinsic growth rates. We have considered the continuous harvesting of predator only. It is observed that if the intrinsic growth rate of predator population crosses a certain critical value, the system enters into Hopf bifurcation. Our observations indicate that tax, the management object in fisheries system play huge impacts on this system. The optimal harvesting policy is disposed by imposing a tax per unit of predator biomass. The optimal harvest strategy is determined using Pontryagin's maximum principle, which is subject to state equations and control limitations. The implications of tax are also examined. We have derived different bifurcations and global stability of the system. Finally, numerical simulations are used to back up the analytical results. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
21460957
Volume :
13
Issue :
1
Database :
Complementary Index
Journal :
International Journal of Optimization & Control: Theories & Applications
Publication Type :
Academic Journal
Accession number :
162617621
Full Text :
https://doi.org/10.11121/ijocta.2023.1218