Bifurcation analysis in a hematopoietic model with delayed Feedback

In this paper, a hematopoietic model is considered. The distribution of the eigenvalues is investigated, and hence a bifurcation set is provided in an appropriate parameter plane. It is found that there are stability switches when the parameter varies, and Hopf bifurcations occur when the parameter passes through a sequence of critical values. Furthermore, the stability and direction of the Hopf bifurcation are determined by applying the normal form and center manifold theory. Then, some numerical simulations are performed to illustrate the analytic results.