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Phase synchronization of three locally coupled chaotic electrochemical oscillators: enhanced phase diffusion and identification of indirect coupling.

Experiments are carried out with three locally coupled phase coherent chaotic electrochemical oscillators (A-B-C) in nickel dissolution in sulfuric acid. As the interaction strength is increased among the electrodes, an onset of synchronization is observed where the frequencies become identical and the phase differences are bounded. The precision of the period of the oscillators is characterized by phase diffusion coefficients from phases and phase differences. The transition to synchronization with increase of coupling strength was found to be accompanied by enhanced phase fluctuations that cause the precision of the oscillations to deteriorate. A parallel synchrony analysis showed that the direct (between A and B and B and C) and the indirect (between A and C) couplings can be correctly identified with the use of a partial phase synchrony index; therefore, the network topology can be deduced from dynamical measurements. Numerical simulations with a locally coupled model for electrochemical chaos confirm the presence of enhanced phase fluctuations close to the transition to synchronization and the usefulness of the partial phase synchrony index for differentiation of direct from indirect interactions in a small network of oscillators.