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

• Published in: An international journal of optimization and control Vol. 13; no. 1; pp. 68 - 80
• Main Authors: Chatterjee, Anal, Pal, Samares
• Format: Journal Article
• Language: English
• Published: Balikesir Balikesir University, Faculty of Engineering Department of Industrial Engineering 01.01.2023
• Subjects: Age groups; Biomass; Commercial fishing; Control theory; Ecosystems; Equations of state; Equilibrium; Fish; Fisheries; Fisheries management; Fishing; Food chains; Hopf bifurcation; Mathematical models; Maximum principle; Optimal control; Predator-prey simulation; Predators; Taxation
• ISSN: 2146-0957; 2146-5703
• DOI: 10.11121/ijocta.2023.1218

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.