Stability and bifurcation analysis in a delayed predator-prey model with harvesting

In this paper, we investigate a delayed stage-structured predator-prey model with continuous harvesting on the prey and Ivlev´s functional response. Positivity and boundness of solutions are obtained. Furthermore, we investigate the stability and Hopf bifurcations by analyzing the distribution of the roots of associated characteristic equation. A explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory.