  Onset and loss of synchronization in coupled oscillators are of fundamental
importance in understanding emergent behavior in natural and man-made systems,
which range from neural networks to power grids. We report on experiments with
hundreds of strongly coupled photochemical relaxation oscillators that exhibit
a discontinuous synchronization transition with hysteresis, as opposed to the
paradigmatic continuous transition expected from the widely used weak coupling
theory. The resulting first-order transition is robust with respect to changes
in network connectivity and natural frequency distribution. This allows us to
identify the relaxation character of the oscillators as the essential parameter
that determines the nature of the synchronization transition. We further
support this hypothesis by revealing the mechanism of the transition, which
cannot be accounted for by standard phase reduction techniques.
