Hysteresis Experiments in Coupled Oscillators near Daido's Aging Transition

One way to experimentally characterize collective oscillations is to measure the magnitude of the steady-state response. In order to examine more dynamic aspects of the behavior, we have measured the hysteresis of the collective response as we vary the collective bifurcation value. Specifically, in our collection of electronic oscillators, we produce a hysteresis by sequentially lowering then raising the bifurcation setting of each oscillator such that the collective bifurcation parameter goes below and above is critical value. The shape of the hysteresis loop exhibits a strong dependence on the rate at which we drive the system through the transition. We find that the area of the hysteresis loop exhibits a square-root dependence on the driving frequency. This is in contrast to feromagnetic and feroelectric systems, which exhibit power-law frequency dependence with much weaker exponents.