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

TL;DR

This paper investigates how repulsive coupling in electrochemical oscillators near a saddle-loop bifurcation leads to partial synchronization, supported by experiments and a phenomenological model that predicts heteroclinic cycle dynamics.

Contribution

It introduces a novel understanding of partial synchronization driven by repulsive coupling near a saddle-loop bifurcation, combining experimental results with a theoretical integrate-and-fire model.

Findings

Repulsive coupling induces synchronized oscillations in electrochemical systems.

Partially synchronized states emerge via heteroclinic cycles between out-of-phase clusters.

The phenomenological model accurately captures waveform and synchronization patterns.

Abstract

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.