Bistable microelectrodes with an S-shaped current-voltage characteristic have recently been shown to oscillate under current control, when connected in parallel. In other systems with equivalently coupled bistable components, such oscillatory instabilities have not been reported. In this paper, we derive a general criterion for when an ensemble of coupled bistable components may become oscillatorily unstable. Using a general model, we perform a stability analysis of the ensemble equilibria, in which the components always group in three or fewer clusters. Based thereon, we give a necessary condition for the occurrence of collective oscillations. Moreover, we demonstrate that stable oscillations may persist for an arbitrarily large number of components, even though, as we show, any equilibrium with two or more components on the middle, autocatalytic branch is unstable.
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