Advances of oscillations in Hopf bifurcation revisited

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.