Abstract
In this paper, we have considered a prey-predator model with stage-structure for predator and selective harvesting of prey species. A regulatory agency controls exploitation by imposing a tax per unit biomass of the prey species. The existence of steady states and their stability are studied. The problem of optimal harvesting policy is solved by using Pontryagin's maximal principle. It is also shown that time delay may cause a stable equilibrium to become unstable. Finally, some numerical simulations are carried out.
Highlights
In a fully dynamic model of an open-access fishery, the level of fishing effort expands or contracts according as the net economic revenue to the fisherman is positive or negative
We study a dynamic reaction model of a prey-predator system where the selective harvesting of prey species is considered
In absence of discrete time delay we investigate the stability of the model system around the interior equilibrium and optimal harvesting policy
Summary
In a fully dynamic model of an open-access fishery, the level of fishing effort expands or contracts according as the net economic revenue to the fisherman is positive or negative. Chaudhuri (1986), Leung (1995), Dai and Tang (1998), Jerry & Raissi (2001), Kar & Chaudhuri (2004), Kar (2006) and some other authors have discussed the prey-predator system with harvesting They have not considered stage structure of species. The rest of the paper is organized as follows: a stage-structured prey-predator model with discrete time delay and harvesting is established . Equilibria and their stability, optimal harvesting policy are discussed in the third section.
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