Synchronization and clustering of arrays of electrochemical oscillators

The collective dynamics of a heterogeneous reacting system affected by global coupling, feedback and external forcing are explored.; The electrodissolution of nickel in sulfuric acid using an array of nickel electrodes under potentiostatic control is studied. We design such an experimental study carried out with an apparatus consisting of an array of 64 electrochemical oscillators and a mechanism of independently changing the global coupling strength among the elements.; The effect of global coupling on both periodic and chaotic oscillators is studied. Maximal global coupling synchronizes both types of oscillators. In the case of coupled periodic oscillators clustering also occurs at some parameter values and these clusters can be made up of periodic or irregular behavior. In the case of coupled chaotic oscillators a uniform low-dimensional chaos occurs for strong coupling. As the coupling strength is decreased the uniform condition is broken, spatial variations arise, and the overall reaction rate becomes generally but not monotonically more complex. At intermediate values of the coupling strength clusters with a variety of configurations occur.; To study the effect of global stimulus on chaotic oscillators, two separate sets of experiments, global feedback and external forcing, are applied to the system through variations in the applied potential.; Clustering and synchronization can be obtained via external periodic forcing in some frequency and amplitude regimes, especially when the forcing frequency is chosen to be equal to one or multiples of that of the basic chaotic motion. The synchronized periodic state is reached via a reverse period doubling temporally, and a spatial condensation of multiple periodic clusters.; Increasing of feedback gain also leads to clustering and synchronization of the system. However, in contrast to external forcing, as the feedback gain is increased, one of the periodic clusters becomes dominating until the periodic synchronized state is obtained.; Both experimental study and model analysis have shown that the application of three apparently different types of global interactions (global coupling, external forcing, and feedback) lead to similar sequences of spatiotemporal behavior: from turbulence to clustering and finally to synchronization, and the differences arising in their paths and the final dynamic states.