  In this paper, we modify the Langevin dynamics associated to the generalized
Curie-Weiss model by introducing noisy and dissipative evolution in the
interaction potential. We show that, when a zero-mean Gaussian is taken as
single-site distribution, the dynamics in the thermodynamic limit can be
described by a finite set of ODEs. Depending on the form of the interaction
function, the system can have several phase transitions at different critical
temperatures. Because of the dissipation effect, not only the magnetization of
the systems displays a self-sustained periodic behavior at sufficiently low
temperature, but, in certain regimes, any (finite) number of stable limit
cycles can exist. We explore some of these peculiarities with explicit
examples.
