On the dynamics of the singularly perturbed Mackey-Glass equation

In this paper, we consider the singularly perturbed Mackey-Glass equation. By letting the perturbation parameter tends to zero, such an equation is formally reduced to a scalar difference equation. Local stability analysis of fixed points is investigated. The method of steps is employed to discretize the system. Moreover, numerical simulations including Lyapunov exponent, bifurcation diagrams and phase portraits are carried out to confirm the theoretical analysis obtained and to explore more complex dynamics of the system.