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A Dynamic Reaction Model of A Prey-Predator System Incorporating a Constant Prey Refuge

Uttam Das, Srabani Guria, T.K. Kar, U. K. Pahari

Abstract



In this paper we consider a dynamic reaction model of a prey-predator system incorporating a constant prey refuge. We have analyzed the boundedness of the system, existence of interior equilibrium and discussed local as well as global stabilities at interior equilibrium of the system. The occurrence of Hopf bifurcation of the system is examined by considering density-dependent mortality for the predator as bifurcation parameter. We have also discussed the influence of prey refuge. The optimal taxation policy is formulated and solved with the help of Pontryagin’s maximal principal. Some numerical simulations are carried out to draw for the validity of our theoretical results.

Keywords


Prey-predator, Prey refuge, Global stability, Harvesting, Optimal taxation.

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