International Journal of Differential Equations
Volume 2011 (2011), Article ID 978387, 25 pages
Research Article

Direction and Stability of Bifurcating Periodic Solutions in a Delay-Induced Ecoepidemiological System

Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India

Received 6 May 2011; Accepted 5 July 2011

Academic Editor: Xingfu Zou

Copyright © 2011 N. Bairagi. 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.


A SI-type ecoepidemiological model that incorporates reproduction delay of predator is studied. Considering delay as parameter, we investigate the effect of delay on the stability of the coexisting equilibrium. It is observed that there is stability switches, and Hopf bifurcation occurs when the delay crosses some critical value. By applying the normal form theory and the center manifold theorem, the explicit formulae which determine the stability and direction of the bifurcating periodic solutions are determined. Computer simulations have been carried out to illustrate different analytical findings. Results indicate that the Hopf bifurcation is supercritical and the bifurcating periodic solution is stable for the considered parameter values. It is also observed that the quantitative level of abundance of system populations depends crucially on the delay parameter if the reproduction period of predator exceeds the critical value.