A note on the calculation of paths of Hopf bifurcations

摘要

This paper is concerned with the analysis of a two parameter nonlinear problem whose linearisation has a double zero eigenvalue with only one eigenvector. The aim of the paper is to present a new approach to the theoretical and computational analysis of the bifurcating branches at this singular point using a symmetry in the system used to calculate Hopf bifurcations. It is shown that standard branch-switching can be used to jump on to the path of Hopf bifurcations emanating from the singular point.