Numerical dynamics of a nonstandard finite difference method for a class of delay differential equations

This paper proposes a nonstandard finite difference (NSFD) method for a class of delay differential equations. We prove that, for any step size h = 1 / m ( m ∈ Z + ), this numerical method could intrinsically preserve the qualitative behavior of the dynamical system, including the local stability of equilibrium, the existence and the direction of Hopf bifurcation and the stability of bifurcating periodic solution. Finally, to illustrate the analytic results, the NSFD method is used for a model of the survival of red blood cells in animals.