Noise-induced periodicity in networks of interacting diffusions

In this thesis we investigate the emergence of collective periodic behaviors in a frustrated network of stochastic interacting diffusions. We provide a model of noisy interacting particles, arranged in two communities of units, which depend on their mutual coupling interactions. Motivated by insights on numerical simulations, we show that this model features the phenomenon of noise-induced periodicity: when the number of particles goes to infinity, in a certain range of interaction strengths, although the system has no periodic behavior in the zero-noise limit, a moderate amount of noise may generate attractive periodic rules