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The dynamics of a system formed by a finite number $N$ of globally coupledbistable oscillators and driven by external forces is studied focusing on aglobal variable defined as the arithmetic mean of each oscillator variable.Several models based on truncation schemes of a hierarchy of stochasticequations for a set of fluctuating cumulant variables are presented. Thishierarchy is derived using It\^o stochastic calculus, and the noise terms in itare treated using an asymptotic approximation valid for large $N$. In addition,a simplified one-variable model based on an effective potential is alsoconsidered. These models are tested in the framework of the phenomenon ofstochastic resonance. In turn, they are used to explain in simple terms thevery large gains recently observed in these finite systems.

Finite size fluctuations and stochastic resonance in globally coupled bistable systems