Abstract
The authors study the oscillations of bistable components and interpret the stationary states of the individual components as electrical circuits to derive a necessary condition for the occurrence of collective oscillations.
Highlights
In contrast to ensembles of coupled oscillators, which have been extensively studied for decades, we have just started to recognize the variety of responses coupled bistable components can exhibit
Oscillations were observed in such all-to-all connected ensembles of a few bistable components at fixed parameter values [11]. This finding was the motivation of the present study, where we derive a necessary condition for the occurrence of a Hopf bifurcaton in systems composed of all-to-all connected generic bistable components and demonstrate that oscillatory dynamics may persist in the macroscopic limit
We have presented a general mechanism of how an oscillation can emerge from an ensemble of globally coupled bistable, nonresonant components
Summary
In contrast to ensembles of coupled oscillators, which have been extensively studied for decades, we have just started to recognize the variety of responses coupled bistable components can exhibit. Individual, sufficiently small electrodes trace out the S-shaped current-voltage equilibrium under current control [14] This is the behavior we consider for an individual, bistable component in our general model. Starting at a low value of the total current where all the partial currents attain the same low value, a slow current ramp induces one electrode after the other to undergo a transition from the low- to the high-current state These sequential transitions might occur in two different ways: In the simpler scenario, each individual electrode resumes one of the three steady states of the S-shaped current-potential curve, the voltage adopting correspondingly to a fixed value within the hysteretic region [5]. Our results elucidate whether important technologically relevant systems, e.g., in catalysis or electrocatalysis where the catalytically active ma-
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