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In this paper, we modify the Langevin dynamics associated to the generalizedCurie-Weiss model by introducing noisy and dissipative evolution in theinteraction potential. We show that, when a zero-mean Gaussian is taken assingle-site distribution, the dynamics in the thermodynamic limit can bedescribed by a finite set of ODEs. Depending on the form of the interactionfunction, the system can have several phase transitions at different criticaltemperatures. Because of the dissipation effect, not only the magnetization ofthe systems displays a self-sustained periodic behavior at sufficiently lowtemperature, but, in certain regimes, any (finite) number of stable limitcycles can exist. We explore some of these peculiarities with explicitexamples.

Coexistence of stable limit cycles in a generalized Curie-Weiss model with dissipation