TITLE:
Hopf Bifurcation Analysis for a Modified Time-Delay Predator-Prey System with Harvesting
AUTHORS:
Yang Ni, Yan Meng, Yiming Ding
KEYWORDS:
Hopf Bifurcation, Time-Delay, Predator-Prey Model
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.7,
June
30,
2015
ABSTRACT: In this paper, we consider the direction
and stability of time-delay induced Hopf bifurcation in a delayed predator-prey
system with harvesting. We show that the positive equilibrium point is
asymptotically stable in the absence of time delay, but loses its stability via
the Hopf bifurcation when the time delay increases beyond a threshold. Furthermore,
using the norm form and the center manifold theory, we investigate the
stability and direction of the Hopf bifurcation.