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The oscillatory response of the potential was monitored in two electrochemical reactions carried out under galvanostatic conditions. In the oxidation of formaldehyde, incrementing the current generated a sequence of temporal states consisting of alternating intervals of periodic and chaotic behaviors. A sequence of periodic states, which obeys Farey addition, was found in the oxidation of formate/formic acid. The temporal states in both reactions consisted of different combinations of small and large oscillations. The observation of these mixed oscillations implies that the kinetic mechanisms contain at least two coupled instabilities.

We analyze measurements of an oscillatory current in an electrochemical process in which copper dissolves into phosphoric acid from a rotating-disk electrode. The focus is on a set of states in which each member consists of a different combination of large and small oscillations (mixed-mode oscillations). This set of mixed-mode oscillations is shown to constitute a Farey sequence, i.e., a periodic sequence for which a one-to-one correspondence exists with an ordered sequence of rational numbers. Plots of a measured quantity known as the ‘‘firing number’’ are presented which reveal a structure that is similar to a ‘‘devil’s staircase.’’ The states surrounding the mixed-mode oscillations are analyzed by examining one-dimensional maps, surfaces of section, and phase portraits constructed from experimental data. This analysis shows that the Farey sequence of these mixed-mode oscillations is of a different nature than the Farey sequences associated with phase locking on a torus.

We describe a sequence of alternating periodic and chaotic behaviors that occur in the anodic dissolution of copper from a rotating disk in phosphoric acid. Each dynamical state of the sequence possesses a different combination of large and small amplitude oscillations (mixed-mode oscillations). The sequence is generated by incrementing either the potential or rotation speed of the copper-disk electrode. We find that chaotic regimes are linked to periodic regimes through tangent and period-doubling bifurcations. Measured waveforms of the chaotic mixed-mode oscillations can appear as mixtures of the waveforms of the adjacent periodic states. Phase portraits and one-dimensional maps are used to characterize a transition to chaotic mixed-mode oscillations from small amplitude chaotic oscillations. A brief comparison is made with the sequences of mixed-mode oscillations found in the Belousov–Zhabotinski reaction.

The response of the current to an applied potential was monitored in an open electrochemical system consisting of a rotating copper disk as the working electrode, a calomel reference electrode, and a platinum counter electrode, all of which were in contact with a solution of 85% phosphoric acid. In addition to stable stationary states, the applied potential induced oscillatory states which were either periodic or chaotic. Transitions from a stationary state to sustained oscillations were found to take place either through a Hopf bifurcation or by way of a mechanism that gives rise to states possessing complex combinations of small and large amplitude oscillations (mixed-mode oscillations). Within the parameter ranges for which sustained oscillations occurred, we discovered sequences of period doubling bifurcations. Aperiodic oscillations were observed just beyond the limit at which a sequence terminated. Phase trajectories were constructed from time-series data for these aperiodic states from which we produced one-humped, one-dimensional maps. A trajectory was also constructed that closely resembled a homoclinic orbit. Mixed-mode oscillations were found which have the same properties as those previously observed in the Belousov–Zhabotinskii reaction. The production of copper was observed in this electrochemical system which suggests that the reaction of disproportionality may be part of a feedback mechanism that is responsible for the complex dynamical behavior.

Sustained voltammetric responses, with periods 2-12 times longer than the period of the cycling potential, were found in application of cyclic voltammetry to the oxidation of methanol at a rotating platinum disk in alkaline solution. Experiments were conducted in which a control parameter (the upper potential limit of the potential cycle) was varied. The results demonstrate that the periodic states are ordered in the same way as dynamical states with the same symbolic representations are ordered in a combined forward and reverse U-sequence. Between ranges of the bifurcation parameter for which periodic states were observed, aperiodic behavior was found that possessed properties that are characteristic of deterministic chaos. High-order periodic responses were also obtained in experiments in which the system was allowed to relax under fixed conditions following the transfer of the Pt electrode to the methanol solution. These results provide evidence that the high-order periodic states do not arise from a slow aging process but, instead, are a consequence of the electrochemical mechanism for the voltammetric oxidation of methanol.

A variety of nonlinear phenomena, which was observed during the electrochemical oxidation of formaldehyde at a rotating platinum disk, is described. The experiments were conducted under galvanostatic conditions and the applied current was treated as a bifurcation parameter. The oxidation process exhibited bistability; both high-potential and low-potential states were found within the same range of values of current. However, most of the low-potential stationary behavior was either nonexistent or unstable in the region of coexistence and, instead, oscillations were observed. Period-doubling bifurcations, leading to chaos, were found by changing the current. Waveforms were recorded that represented dynamical states belonging to a periodie-chaotic sequence which was previously characterized under other conditions. The results presented here include dynamical states that were measured further into the sequence. New types of states within the sequence were also discovered. These latter states possessed characteristics that made them appear similar to dynamical states recently measured in an experimental investigation of the oxidation of formic acid. However, an examination of their symbolic patterns, which were obtained from one-dimensional mappings, reveals that they were different. The observation of yet other types of oscillations suggests that the oxidation of formaldehyde is coupled to more than one of the stages of the process in which oxide layers are formed on the platinum electrode.