Table of Contents
ISRN Biomathematics
Volume 2013, Article ID 637640, 12 pages
http://dx.doi.org/10.1155/2013/637640
Research Article

Global Dynamics of an Exploited Prey-Predator Model with Constant Prey Refuge

1Department of Mathematics, Sree Chaitanya College, Habra, North 24 Parganas 743268, India
2Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah 711103, India

Received 27 May 2013; Accepted 8 July 2013

Academic Editors: M. T. Figge, M. José, A. A. Polezhaev, and J. H. Wu

Copyright © 2013 Uttam Das et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper describes a prey-predator model with Holling type II functional response incorporating constant prey refuge and harvesting to both prey and predator species. We have analyzed the boundedness of the system and existence of all possible feasible equilibria and discussed local as well as global stabilities at interior equilibrium of the system. The occurrence of Hopf bifurcation of the system is examined, and it was observed that the bifurcation is either supercritical or subcritical. Influences of prey refuge and harvesting efforts are also discussed. Some numerical simulations are carried out for the validity of theoretical results.