  We modify the spin-flip dynamics of a Curie-Weiss model with dissipative
interaction potential (Dai Pra, Fischer and Regoli (2013)) by adding a
site-dependent i.i.d. random magnetic field. The purpose is to analyze how the
addition of the field affects the time-evolution of the observables in the
macroscopic limit. Our main result shows that a Bautin bifurcation point exists
and that, whenever the field intensity is sufficiently strong and the
temperature sufficiently low, a periodic orbit emerges through a global
bifurcation in the phase space, giving origin to a large-amplitude rhythmic
behavior.
