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.