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 JAMP  Vol.3 No.7 , July 2015
Hopf Bifurcation Analysis for a Modified Time-Delay Predator-Prey System with Harvesting
Yang Ni, Yan Meng, Yiming Ding
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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.
Keywords: Hopf Bifurcation, Time-Delay, Predator-Prey Model
Cite this paper: Ni, Y. , Meng, Y. and Ding, Y. (2015) Hopf Bifurcation Analysis for a Modified Time-Delay Predator-Prey System with Harvesting. Journal of Applied Mathematics and Physics, 3, 771-780. doi: 10.4236/jamp.2015.37094.
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