CHAOS, NOISE, AND SYNCHRONIZATION

We show that a pair of chaotic systems subjected to the same noise may undergo a transition at large enough noise amplitude and follow almos t identical trajectories with complete insensitivity to initial condit ions. An analytic argument is presented to show that a pair of generic systems in the same potential evolving to equilibrium through standar d Langevin dynamics with the same noise collapse into the same traject ory at long times.