Open Access Open Access  Restricted Access Subscription or Fee Access

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

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


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.


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

Full Text:



  • There are currently no refbacks.

Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.