Coupled Brownian Motors: anomalous-to-normal hysteresis transition and noise induced limit cycle

We study a model consisting of $N$ nonlinear oscillators with "global periodic" coupling and "local multiplicative" and additive noises. The model was shown to undergo a nonequilibrium phase transition towards a broken-symmetry phase exhibiting noise-induced ``ratchet" behavior. Here we review some aspects leading to an ''anomalous--to--normal" transition in the ratchet's hysteretic behavior and also show --as suggested by the absence of stable solutions when the load force is beyond a critical value-- the existence of a limit cycle induced by both: multiplicative noise and "global periodic" coupling.