Hopf Bifurcation Analysis for a Modified Time-Delay Predator-Prey System with Harvesting

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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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