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Analytical and Numerical Studies of Noise-induced Synchronization of Chaotic Systems

Toral, Raúl; Mirasso, Claudio; Hernández-García, Emilio; Piro, Oreste
Chaos 11, 665-673 (2001)

We study the effect that the injection of a common source of noise
has on the trajectories of chaotic systems, addressing some
contradictory results present in the literature. We present
particular examples of 1-d maps and the Lorenz system, both in the
chaotic region, and give numerical evidence showing that the
addition of a common noise to different trajectories, which start
from different initial conditions, leads eventually to their
perfect synchronization. When synchronization occurs, the largest
Lyapunov exponent becomes negative. For a simple map we are able
to show this phenomenon analytically. Finally, we analyze the
structural stability of the phenomenon.