Dynamics of a discrete food-limited population model with time delay

In this paper, we consider a discrete food-limited population model with time delay. Firstly, the stability of the equilibrium of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that Neimark-Sacker bifurcations occur when the delay passes a sequence of critical values. Then the explicit algorithm for determining the direction of the Neimark-Sacker bifurcations and the stability of the bifurcating periodic solutions are derived. Finally, some numerical simulations are given to verify the theoretical analysis.