In this paper, we propose and analyze a three-species predator prey system in the presence of additional food for top predator. It is assumed that the middle predator is acting as a prey as well as a predator and the ...In this paper, we propose and analyze a three-species predator prey system in the presence of additional food for top predator. It is assumed that the middle predator is acting as a prey as well as a predator and the top predator consumes both prey as well as middle predator. It is also considered that a constant amount of additional food for top predator exists in the ecosystem. The effects of harvesting of top predator are investigated. The existence and stability conditions of the equilibria have been discussed analytically. The Hopf bifurcation analysis of the system with respect to predation rate of prey to the top predator and the harvesting effort have been analyzed both analytically and numerically. Pontryagin＇s maximum principle is used to determine the optimal harvesting of top predator population to maximize the discounted net revenue. From our analysis, it is seen that the additional food has a significant impact to prevent the extinction risk of top predator population and also to increase revenue collection. Finally, some numerical results have been given in support of our analytical findings.展开更多
文摘In this paper, we propose and analyze a three-species predator prey system in the presence of additional food for top predator. It is assumed that the middle predator is acting as a prey as well as a predator and the top predator consumes both prey as well as middle predator. It is also considered that a constant amount of additional food for top predator exists in the ecosystem. The effects of harvesting of top predator are investigated. The existence and stability conditions of the equilibria have been discussed analytically. The Hopf bifurcation analysis of the system with respect to predation rate of prey to the top predator and the harvesting effort have been analyzed both analytically and numerically. Pontryagin＇s maximum principle is used to determine the optimal harvesting of top predator population to maximize the discounted net revenue. From our analysis, it is seen that the additional food has a significant impact to prevent the extinction risk of top predator population and also to increase revenue collection. Finally, some numerical results have been given in support of our analytical findings.
