Stability and bifurcation analysis on a Logistic model with discrete and distributed delays

In this paper, a Logistic model with discrete and distributed delays is investigated. We first consider the stability of the positive equilibrium and the existence of local Hopf bifurcations. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions. A numerical simulation for supporting the theoretical analysis is also given.