Singular Hopf bifurcation to unstable periodic solutions in a NMR laser

We apply recent developments in the study of singular Hopf bifurcations to describe the complete bifurcation diagram of a simple NMR laser with an injected signal. The branch of periodic solutions appears at a Hopf bifurcation point and may or may not disappear at a homoclinic point. The bifurcation is always subcritical, which suggests that the periodic solutions are all unstable. Our asymptotic analysis is based on the relative values of the fixed parameters in the problem. Our results complement earlier investigations by Holzner et al. [Phys. Rev. A 36, 1280 (1987)] and by Baugher, Hammack, and Lin [Phys. Rev. A 39, 1549 (1989)] on the subcritical Hopf bifurcation in a NMR laser.