Experiments on Arrays of Globally Coupled Periodic Electrochemical Oscillators

Experiments on periodically oscillating arrays consisting of from one to 64 nickel electrodes in sulfuric acid are carried out. Harmonic and relaxation oscillations that occur respectively in two regions of parameter space are considered. External resistors in parallel and series are added to vary the extent of global coupling among the oscillators. The array is heterogeneous due to small variations in the properties of the electrodes, and there is also a small amount of noise. With no added global coupling there is a narrow distribution in frequency of the oscillators. As global coupling is added to the arrays of harmonic oscillators the distribution of frequencies become narrower until synchronization is attained; further increase brings the phases together. There is no qualitative change in the dynamics of an individual element. Coupling of the relaxation oscillators leads to more complicated behavior. As the global coupling strength is increased from zero there is a tendency for the system to synchronize, but this synchronized state then breaks up with increasing coupling. Irregular behavior including transient clusters then occurs. At stronger coupling the clusters become stable; these stable clusters can consist of individual currents that are either irregular or periodic with higher period. Multistability occurs in this region, i.e, many cluster configurations are possible. At higher coupling strengths antiphase oscillations occur where the clusters are made up of equal or approximately equal number of oscillators. Strong coupling synchronizes the oscillators. Simulations based on coupled electrochemical oscillators reproduced many of the dynamical features.