alexa Global dynamics and bifurcation in a stage structured prey–predator fishery model with harvesting
Agri and Aquaculture

Agri and Aquaculture

Fisheries and Aquaculture Journal

Author(s): Kunal Chakraborty, Soovoojeet Jana, TK Kar

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This paper describes a prey–predator model with stage structure for predator and selective harvesting effort on predator population. The Holling type II functional response function is taken into consideration. All the equilibria of the proposed system are determined and the behavior of the system is investigated near them. Local stability of the system is analyzed. Geometric approach is used to derive the sufficient conditions for global stability of the system. The occurrence of Hopf bifurcation of the model system in the neighborhood of the co-existing equilibrium point is shown through considering maximal relative increase of predation as bifurcation parameter. Fishing effort used to harvest predator population is considered as a control to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent earned from the resource. Pontryagin’s maximum principle is used to characterize the optimal control. The optimal system is derived and then solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem.

This article was published in Applied Mathematics and Computation and referenced in Fisheries and Aquaculture Journal

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