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In this paper, we discuss the special diffusive hematopoiesis model  $$\frac{{\partial P(t,x)}}{{\partial t}} = \Delta P(t,x) - \gamma P(t,x) + \frac{{\beta P(t - \tau ,x)}}{{1 + P^n (t - \tau ,x)}}$$  with Neumann boundary condition. Sufficient conditions are provided for the global attractivity and oscillation of the equilibrium for Eq. (*), by using a new theorem we stated and proved. When P(t, χ) does not depend on a spatial variable χ ∈ Ω, these results are also true and extend or complement existing results. Finally, existence and stability of the Hopf bifurcation for Eq. (*) are studied.

Global attractivity, oscillation and Hopf bifurcation for a class of diffusive hematopoiesis models