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 relaxatio n oscillations that occur respectively in two regions of parameter space ar e considered. External resistors in parallel and series are added to vary t he extent of global coupling among the oscillators. The array is heterogene ous 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 n arrow distribution in frequency of the oscillators. As global coupling is a dded 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 i ndividual element. Coupling of the relaxation oscillators leads to more com plicated behavior. As the global coupling strength is increased from zero t here is a tendency for the system to synchronize, but this synchronized sta te then breaks up with increasing coupling. irregular behavior including tr ansient clusters then occurs. At stronger coupling the clusters become stab le; these stable clusters can consist of individual currents that are eithe r irregular or periodic with higher period. Multistability occurs in this r egion, i.e, many cluster configurations are possible. At higher coupling st rengths antiphase oscillations occur where the clusters are made up of equa l or approximately equal number of oscillators. Strong coupling synchronize s the oscillators. Simulations based on coupled electrochemical oscillators reproduced many of the dynamical features.