On the Hopf-zero bifurcation of the Michelson system

Applying a new result for studying the periodic orbits of a differential system via the averaging theory, we provide the first analytic proof of the existence of a Hopf-zero bifurcation for the Michelson system ẋ=y,ẏ=z,ż=c2−y−x22, at c=0c=0. Moreover our method estimates the shape of this periodic orbit as a function of c>0c>0, sufficiently small.