An experimental study of a population of relaxation oscillators with a phase-repelling mean-field coupling

The dynamical behavior of a system of coupled relaxation oscillators is studied experimentally. A population of up to 15 coupled electronic op-amp relaxation oscillators is used as a prototype for the real collections of limit-cycle oscillators frequently found in many physical, biological, and technological systems. The oscillators interact via an all-to-all or mean-field coupling. The rarely studied case of antiferromagnetic interactions, in which oscillators tend to repel each other in phase, is considered. The behavior of the system is significantly different from the predictions of the limited theory that is currently available. The novel behavior observed includes the existence of numerous distinguishable phase-locked states and an exponential distribution of the duration of transients. The critical coupling strength necessary for the oscillator system to completely phase-lock is measured. A simple geometrical model of the dynamics of the system during the transient is presented as a means of understanding the exponential distribution of transient lengths. In addition, a phase-response oscillator model is shown to exhibit similar transient behavior.