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Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays

Xu C., Liao M., He X.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 1

97-107

In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations for supporting the theoretical results are also included.