Table of Contents
Journal of Nonlinear Dynamics
Volume 2014, Article ID 543041, 10 pages
http://dx.doi.org/10.1155/2014/543041
Research Article

Bifurcation Analysis of a Delayed Predator-Prey Model with Holling Type III Functional Response and Predator Harvesting

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

Received 26 August 2013; Revised 10 January 2014; Accepted 21 January 2014; Published 3 March 2014

Academic Editor: Dibakar Ghosh

Copyright © 2014 Uttam Das and T. K. Kar. 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 tries to highlight a delayed prey-predator model with Holling type III functional response and harvesting to predator species. In this context, we have discussed local stability of the equilibria, and the occurrence of Hopf bifurcation of the system is examined by considering the harvesting effort as bifurcation parameter along with the influences of harvesting effort of the system when time delay is zero. Direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also studied by applying the normal form theory and the center manifold theorem. Lastly some numerical simulations are carried out to draw for the validity of the theoretical results.