Emergence of self-sustained oscillations in mean-field models with dissipation

In this thesis we present a version of the Curie-Weiss model where the standard mean-field interaction is perturbed by a dissipative term. We prove that the model in the thermodynamic limit shows a phase transition from a regime where the magnetization is constant close to zero to a regime where periodic oscillations emerge. Next we extend the results to the generalized Curie-Weiss model where each spin is a random variable taking values in the reals. We study the thermodynamic limit and the long-time behavior of the system, in particular for the Gaussian case, with and without the dissipation.