Optimization Induced Collective Behavior in a System of Flashing Oscillators

Abstract

An array of pulse-emitting oscillators capable of emerging collective behavior is investigated by computer simulations and through a simple experimental setup. The oscillators emit pulse-like signals and detect the signal emitted by the others. They have stochastically fluctuating periods and can operate in two different modes, one with a short output pulse and one with a longer one. The switching between modes is governed by a simple optimization rule: whenever the total output in the system is lower than a desired f * threshold level they emit long pulses and when the output is higher than f * they emit short-length pulses. This simple dynamical rule optimizes the average output level in the system around the f * value and acts as a coupling between the units. As a side-effect of this simple dynamics complex collective behavior appears. In spite of the fact that there is no direct phase-minimizing interaction between the units, for a certain f * interval the pulses of the oscillators synchronize. Synchronization appears and disappears abruptly as a function of the f * threshold parameter, suggesting a dynamic phase-transition. In the synchronized phase the collective output of the system has a better periodicity than the oscillators individually. A simple experimental setup with flashing multimode oscillators is built. For a given range of the threshold parameter the experimental setup reproduces the theoretically predicted synchronization.