Synchronization and clustering of arrays of electrochemical oscillators with global feedback

Experiments on chaotically oscillating arrays of nickel electrodes in sulfuric acid were carried out. A global feedback is added in which a signal proportional to the difference between the sum of the currents of all elements and a mean current is fed back to the applied potential. The addition of global feedback transforms a system of weakly coupled elements to one of complete synchronization. At intermediate feedback strengths, intermittent, unstable chaotic clusters are observed in which clusters of elements form and break up. Stable clusters or condensates form at somewhat higher feedback strengths. The stable clusters become periodic at higher gain; both two-cluster and three-cluster states are observed. With a further increase in the feedback gain, one of the clusters dominates the collective dynamics; its size increases until at some feedback strength the entire system is synchronized. Delay in the feedback signal also influences the interaction of the oscillators.