Zhang, J., Li, W. and Yan, X. (2011) Hopf Bifurcation and Turing Instability in Spatial Homogeneous and Inhomogeneous Predator-Prey Models. Applied Mathematics & Computation, 218, 1883-1893. http://dx.doi.org/10.1016/j.amc.2011.06.071

has been cited by the following article:

• 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.