In the present paper the non-linear time evolution of the electrodissolution/passivation of iron in sulfuric acid-sodium chloride solution is explored. The working electrode is an assembly of two iron disk electrodes, interacting through the electrolyte, and the time evolution of the electric current has the form of spontaneous bursting oscillations. The main aim of this work is to characterize the modes of synchrony and more specifically the synchronization of electric bursts and the synchronization of electric spikes. The characterization is based on the calculation of the firing rates from the experimental time series and the extraction of the slow dynamics by low-pass filtering. The analysis is performed both for elliptic and square wave electrochemical bursting and the results are compared with neural oscillations.