In this paper, we consider a single-species logistic model with Gamma type continuous time delay and constant inflow. By the linear chain trick, the system of integro-differential equations is transformed into the system of the expanded ordinary differential equations. The results show that the average time delay (order of k≥2) can destabilize the positive equilibrium through Hopf bifurcation. Furthermore, the precise conditions of Hopf bifurcation of the high dimensional system are obtained b...
