Stability analysis of a discrete Hutchinson equation with discrete and distributed delay

In this paper a Hutchinson equation with discrete and distributed delay is discretized by the Euler method. The dynamics of the obtained discrete system is then investigated. Specifically the stability of the positive fixed point is analyzed. It is found that for sufficiently small time-step of integration, the positive equilibrium undergoes a Neimark-Sacker bifurcation which is controlled by the discrete time delay. The results of analysis are then confirmed by some numerical simulations.