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Experiments and supporting theoretical analysis is presented to describe thesynchronization patterns that can be observed with a population of globallycoupled electrochemical oscillators close to a homoclinic, saddle-loopbifurcation, where the coupling is repulsive in the electrode potential. Whileattractive coupling generates phase clusters and desynchronized states,repulsive coupling results in synchronized oscillations. The experiments areinterpreted with a phenomenological model that captures the waveform of theoscillations (exponential increase) followed by a refractory period. Theglobally coupled autocatalytic integrate-and-fire model predicts thedevelopment of partially synchronized states that occur through attractingheteroclinic cycles between out-of-phase two-cluster states. Similar behaviorcan be expected in many other systems where the oscillations occur close to asaddle-loop bifurcation, e.g., with Morris-Lecar neurons.

Partial synchronization of relaxation oscillators with repulsive coupling in autocatalytic integrate-and-fire model and electrochemical experiments