Numerical Hopf bifurcation for a class of delay differential equations

Abstract

In this paper we consider discretization of parameter-dependent delay differential equations of the form x′(t)=f(x(t),x(t−τ),λ), λ∈ R. We show that, if the delay differential equation undergoes a Hopf bifurcation, then the discrete scheme undergoes a Hopf bifurcation of the same type. The results of this paper extend the results of our previous analysis relating to the discretization of the delay logistic equation to a wider class of problems.