Hopf bifurcation in a delayed food-limited model with feedback control

In this paper, we consider a delayed food-limited model with feedback control. By regarding the delay as the bifurcation parameter and analyzing the corresponding characteristic equations, the linear stability of the system is discussed, and Hopf bifurcations are demonstrated. By the normal form and the center manifold theory, the explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. Finally, some examples are presented to verify our main results.