Advances of oscillations in Hopf bifurcation revisited

摘要

This study clarifies some issues regarding advances of oscillations when passage through a Hopf bifurcation is attempted. Specifically, it has been reported before that advances occur when the bifurcation parameter varies slowly through a Hopf bifurcation point. Here it is emphasized that if this variation is sufficiently slow advances are eliminated and an upper bound on the error between the system's trajectory and the branch of equilibria is given.