Fluctuation analysis of synchronized system

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We study the limiting behavior of fluctuations of synchronized system with small noise around their averaged deterministic limit. There are three regimes depending on how fast the intensity of the noise goes to zero relative to coupling parameter. By simple transformations, the original synchronized system is equivalently converted into the slow–fast system, then we derive the central limit theorem of the slow variable by the martingale method. Therefore, the fluctuation properties corresponding to the original synchronized system are derived.