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We modify the spin-flip dynamics of a Curie-Weiss model with dissipativeinteraction potential (Dai Pra, Fischer and Regoli (2013)) by adding asite-dependent i.i.d. random magnetic field. The purpose is to analyze how theaddition of the field affects the time-evolution of the observables in themacroscopic limit. Our main result shows that a Bautin bifurcation point existsand that, whenever the field intensity is sufficiently strong and thetemperature sufficiently low, a periodic orbit emerges through a globalbifurcation in the phase space, giving origin to a large-amplitude rhythmicbehavior.

Effects of local fields in a dissipative Curie-Weiss model: Bautin bifurcation and large self-sustained oscillations