Complexity of globally coupled chaotic electrochemical oscillators

Interactions among small sets of two to eight nickel electrodes undergoing chaotic electrodissolution in sulfuric acid were studied. A single oscillator under these conditions exhibits low-dimensional chaotic behavior. Global coupling among the electrodes was added with the use of external resistors in a manner such that the strength of the coupling could be varied while the other parameters of the system remained constant. Such global coupling is of course equivalent to an appropriate local coupling for the two-electrode system and even for a three-electrode system if arranged in a ring. We investigate the changes in complexities of both the individual oscillators and of the total current as functions of coupling strength and of array size. The dynamics of the individual oscillators are almost identical to those of the single oscillator at added coupling strengths of zero (where the oscillators are almost independent) and at maximum coupling strength (where they are synchronized). There are two trends (with exceptions) with changing coupling strength. (1) The complexity (information dimension) of the individual currents has a maximum at intermediate values of the coupling strength, i.e., at conditions in which interactions occur but where the coupling is not strong enough to produce synchronization. (2) An increase in global coupling decreases the complexity of the total current. The general trends with coupling strength are interrupted by clustering that occurs with the four and eight electrode arrays. Cluster configurations for the larger array exhibiting both chaotic (3,5 cluster) and periodic (4,4 cluster) dynamics were observed.