Stability and bifurcation of a discrete red blood cell survival model

A kind of a discrete red blood cell survival model obtained by Euler method is investigated. Firstly, the linear stability of the model is studied. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Then the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived by using the normal form method and center manifold theorem. Finally, computer simulations are performed to illustrate the analytical results found.