On the analysis of Hopf bifurcation associated with a two-fold zero eigenvalue, Part 1: Autonomous system

Abstract

The static and dynamic bifurcations of an autonomous system associated with a two-fold zero eigenvalue (of index one) are studied. Attention is focused on Hopf bifurcation solutions in the neighborhood of such a singularity. The family of limit cycles are analyzed fully by applying the formula type results of the Intrinsic Harmonic Balancing method. Thus, parameter-amplitude and amplitude-frequency relationships as well as an ordered form of approximations for the periodic motions are obtained explicitly. A verification technique, with the aid of MAPLE, is used to show the consistency of ordered approximations.