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Global dynamics and bifurcation in a stage structured prey-predator fishery model with harvesting

Chakraborty, K and Jana, S and Kar, TK (2012) Global dynamics and bifurcation in a stage structured prey-predator fishery model with harvesting. Applied Mathematics and Computation, 218 (18). pp. 9271-9290.

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Abstract

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.

Item Type: Article
Additional Information: Copyright of this article belongs to Elsevier.
Uncontrolled Keywords: Prey–predator fishery;Stage structure;Harvesting;Hopf bifurcation;Optimal control;Global stability
Subjects: Oceanography > oceanography
Depositing User: INCOIS Library
Date Deposited: 11 Dec 2013 09:42
Last Modified: 11 Dec 2013 09:42
URI: http://moeseprints.incois.gov.in/id/eprint/150

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