Hopf bifurcation in numerical approximation of a class delay differential equations

Abstract In this paper we consider the numerical solution of a delay differential equation undergoing a Hopf bifurcation. We prove that if the delay differential equation has a Hopf bifurcation point at λ = λ * , then the numerical solution of the equation also has a Hopf bifurcation point at λ h = λ * +O( h ).