A new application of the normal form description to a N-dimensional dynamical systems attending the conditions of a Hopf bifurcation

Abstract

In this paper we prove the following theorem: consider a N-dimensional dynamical system that is reduced to its center manifold. If it is proved the system satisfies the conditions of a Hopf bifurcation theorem then the original system of differential equations escribing the dynamics can be rewritten in a simpler analytical expression that preserves the phase space topology. The theorem proposed and proven effectively reduces the work done to obtain the normal form for the class of dynamical systems with the ccurrence of Hopf bifurcation.