Analytical and numerical studies of noise-induced synchronization of chaotic systems

We study the effect that the injection of a common source of noise has on t he trajectories of chaotic systems, addressing some contradictory results p resent in the literature. We present particular examples of one-dimensional maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajecto ries, which start from different initial conditions, leads eventually to th eir perfect synchronization. When synchronization occurs, the largest Lyapu nov exponent becomes negative. For a simple map we are able to show this ph enomenon analytically. Finally, we analyze the structural stability of the phenomenon. (C) 2001 American Institute of Physics.