The collective behavior of an ensemble of multimode stochastic oscillators is investigated. The oscillators are pulse coupled; they are able to emit pulses and to detect the pulses emitted by the others. As a function of the output intensity in the system they can operate in different modes having different pulsing periods. The system is designed to optimize the output intensity around a fixed f* output threshold. In order to do so a simple dynamics is considered. Whenever the total output intensity in the system is lower than f*, a mode with a higher interpulse period is chosen. If the light intensity in the system is higher than f*, a mode with a lower interpulse period is selected. As a side effect of this simple optimization rule, for a given f* interval a nontrivial synchronization of the oscillators is observed. The synchronization level is studied by computer simulations, investigating the influence of model parameters (number of modes, stochasticity of the oscillators, the f* threshold value, and interaction topology). An experimental realization of this system is also considered; an ensemble of electronic oscillators communicating with light pulses was constructed and studied. The experimental system behaves in many ways similar to the theoretically considered multimode stochastic oscillator ensemble.
Spontaneous synchronization of an ensemble of metronomes placed on a freely rotating platform is studied experimentally and by computer simulations. A striking in-phase synchronization is observed when the metronomes' beat frequencies are fixed above a critical limit. Increasing the number of metronomes placed on the disk leads to an observable decrease in the level of the emerging synchronization. A realistic model with experimentally determined parameters is considered in order to understand the observed results. The conditions favoring the emergence of synchronization are investigated. It is shown that the experimentally observed trends can be reproduced by assuming a finite spread in the metronomes' natural frequencies. In the limit of large numbers of metronomes, we show that synchronization emerges only above a critical beat frequency value.
Metronomes placed on the perimeter of a disc-shaped platform, which can freely rotate in a horizontal plane, are used for a simple classroom illustration of the Kuramoto-type phase transition. The rotating platform induces a global coupling between the metronomes, and the strength of this coupling can be varied by tilting the metronomes’ swinging plane relative to the radial direction on the disc. As a function of the tilting angle, a transition from spontaneously synchronized to unsynchronized states is observable. By varying the number of metronomes on the disc, finite-size effects are also exemplified. A realistic theoretical model is introduced and used to reproduce the observed results. Computer simulations of this model allow a detailed investigation of the emerging collective behaviour in this system.
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