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

Raul Toral·Claudio R. Mirasso·Emilio Hernandez-Garcia·Oreste Piro
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Abstract

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.

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Raul Toral, Claudio R. Mirasso, Emilio Hernandez-Garcia, Oreste Piro. 2001-04-18. Analytical and Numerical Studies of Noise-induced Synchronization of Chaotic Systems. https://doi.org/10.1063/1.1386397

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