Controlling Electrochemical Chaos in the Copper−Phosphoric Acid System

Abstract

Model calculations indicate that chaotic current oscillations during anodic electrodissolution of copper into phosphoric acid may be controlled by applying a simple map-based algorithm. In the experiments, the unstable period-one and period-two orbits embedded in the chaotic attractor have been stabilized by small perturbations of the anodic potential. We present the results of an experimental test for a power law relating the average chaotic transient time to the size of maximum perturbation allowed during control. The reported experimental results are in good agreement with the theoretical predictions by Ott, Grebogi, and Yorke.

The control of chaos: theory and applications

“…The OGY method has also been optimized by In et al [185] through an adaptive technique. Furthermore, OGY has been also used by Kiss et al [186] for the control of the electrodissolution of a rotating copper disk in a phosphoric acid electrolite. A recent electrochemical experiment is reported in Ref.…”

Control of Electrochemical Chaos and Unstable Steady-States

“…also Fig. 5 in [10]). The control parameter K for period-two control is À11 mV/mA and dV max is 0.5 mV.…”

“…The potential perturbations dV n (right axis) applied at the successive returns to the Poincaré section are shown in the insert. See [10] for experimental conditions and other details. Reprinted with permission from [10].…”

“…See [10] for experimental conditions and other details. Reprinted with permission from [10]. Copyright 1997 American Chemical Society the perturbation signal is proportional to the time derivative of the appropriate dynamic variable or control parameter.…”

“…The SPF algorithm was further successfully applied by Kiss et al [10] to controlling electrochemical chaos in the copper-phosphoric acid system, both in terms of theoretical calculations (involving the three-variable model by Koper and Gaspard [9]) and experimental results. In particular, the aim of the work was to control chaotic current oscillations at such Cu disk rotation rates where chaos developed through simple period-doubling bifurcations (see Fig.…”