Dynamics of a nonstandard finite-difference scheme for Mackey–Glass system

In this article, we study the dynamics of Mackey–Glass system applied a nonstandard finite-difference scheme. For the discrete system we show that a sequence of Hopf bifurcations occur at the positive fixed point as the delay increasing, analyze the stability of the fixed point and calculate the direction of the Hopf bifurcations. At last, by giving some numerical experiments, we illustrate the relation between the time of producing blood cells and symptom.