Stability analysis of a single-species logistic model with time delay and constant inflow
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 by the method of polar form and graphs.