  Experiments and supporting theoretical analysis is presented to describe the
synchronization patterns that can be observed with a population of globally
coupled electrochemical oscillators close to a homoclinic, saddle-loop
bifurcation, where the coupling is repulsive in the electrode potential. While
attractive coupling generates phase clusters and desynchronized states,
repulsive coupling results in synchronized oscillations. The experiments are
interpreted with a phenomenological model that captures the waveform of the
oscillations (exponential increase) followed by a refractory period. The
globally coupled autocatalytic integrate-and-fire model predicts the
development of partially synchronized states that occur through attracting
heteroclinic cycles between out-of-phase two-cluster states. Similar behavior
can be expected in many other systems where the oscillations occur close to a
saddle-loop bifurcation, e.g., with Morris-Lecar neurons.
