Stability of singular Hopf bifurcations

Abstract A stability formula is given for the singular Hopf bifurcation arising in singularly perturbed systems of the form x ˙ = e f ( x , y , λ ) , y ˙ = g ( x , y , λ ) in this paper. The derivation of the formula is based on a reduction technique and on an existing stability formula for Hopf bifurcation.