A Maple program for computing a terms of a center manifold, and element of bifurcations for a class of retarded functional differential equations with Hopf singularity

Abstract

In this paper, we present explicit formulas for computing the coefficients of a center manifold for the Hopf singularity in autonomous retarded functional differential equations. As consequence, an algorithm for computing Lyapunov constant and normal forms up to an arbitrary order is derived. The explicit formulas have been implemented using the computer algebra system Maple. The paper ends with some examples in order to show the applicability of the methodology and the convenience of the computer software.