Dynamical properties of chemical systems near Hopf bifurcation points

Abstract

In this paper, we numerically investigate local properties of dynamical systems close to a Hopf bifurcation instability. We focus on chemical systems and present an approach based on the theory of normal forms for determining numerical estimates of the limit cycle that branches off at the Hopf bifurcation point. For several numerically ill-conditioned examples taken from chemical kinetics, we compare our results with those obtained by using traditional approaches where an approximation of the limit cycle is restricted to the center subspace spanned by critical eigenvectors, and show that inclusion of higher-order terms in the normal form expansion of the limit cycle provides a significant improvement of the limit cycle estimates. This result also provides an accurate initial estimate for subsequent numerical continuation of the limit cycle.