Tracking unstable steady states and periodic orbits of oscillatory and chaotic electrochemical systems using delayed feedback control

Kiss, István Z.; Kazsu, Zoltán; Gáspár, Vilmos

doi:10.1063/1.2219702

Cited by 34 publications

(34 citation statements)

References 66 publications

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“…At small ohmic drops (often provided by the cell series resistance) bistability is expected [2, 34, 36, 37]. This bistability can be observed in the cyclic polarization scan shown in Figure 2b: in a potential region of 1.11 V < V < 1.16 V a high- and a low-current steady states coexist on the forward and backward polarization scans, respectively.…”

Section: Resultsmentioning

confidence: 96%

“…The rich nonlinear dynamical phenomena of Ni electrodissolution [2, 24, 25, 29, 34-37] have been observed at large overpotentials where the kinetics of transpassive dissolution is further complicated by secondary passivation and O 2 evolution (regions C-E). At small ohmic drops (often provided by the cell series resistance) bistability is expected [2, 34, 36, 37].…”

Section: Resultsmentioning

confidence: 99%

“…The forward polarization voltammogram in the transpassive region (Figure 2c) shows that current oscillations appear on the positive slope of the scan in a circuit potential region of 1.09 V < V < 1.21 V. The onset and disappearance of oscillations with finite frequency and zero amplitude indicates that with small added resistance the oscillations are obtained through Hopf bifurcations; the nature of these bifurcations have been proved by impedance spectroscopy. [2, 34] At potentiostatic conditions the currents exhibit oscillatory behavior; an example is shown in Figure 2d at V =1.130 V. During these oscillations the mean current is 0.47 mA from which we can approximate that the approximate IR potential drop that is needed to induce oscillations is about 80 mV. Note that it is possible to obtain bistability between oscillatory and stationary states because of the overlap of the corresponding regions as shown in the reverse scan in Figure 2c for 1.19V < V <1.21V.…”

Section: Resultsmentioning

confidence: 99%

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Electrochemical oscillations of nickel electrodissolution in an epoxy-based microchip flow cell

Cioffi

Martin

Kiss

2011

Journal of Electroanalytical Chemistry

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We investigate the nonlinear dynamics of transpassive electrodissolution of nickel in sulfuric acid in an epoxy-based microchip flow cell. We observed bistability, smooth, relaxation, and period-2 waveform current oscillations with external resistance attached to the electrode in the microfabricated electrochemical cell with 0.05 mm diameter Ni wire under potentiostatic control. Experiments with 1mm × 0.1 mm Ni electrode show spontaneous oscillations without attached external resistance; similar surface area electrode in macrocell does not exhibit spontaneous oscillations. Combined experimental and numerical studies show that spontaneous oscillation with the on-chip fabricated electrochemical cell occurs because of the unusually large ohmic potential drop due to the constrained current in the narrow flow channel. This large IR potential drop is expected to have an important role in destabilizing negative differential resistance electrochemical (e.g., metal dissolution and electrocatalytic) systems in on-chip integrated microfludic flow cells. The proposed experimental setup can be extendend to multi-electrode configurations; the epoxy-based substrate procedure thus holds promise in electroanalytical applications that require collector-generator multi-electrodes wires with various electrode sizes, compositions, and spacings as well as controlled flow conditions.

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Section: Resultsmentioning

confidence: 96%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Electrochemical oscillations of nickel electrodissolution in an epoxy-based microchip flow cell

Cioffi

Martin

Kiss

2011

Journal of Electroanalytical Chemistry

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“…More recently, Kiss et al [27] have used delayed-feedback control to tracking unstable steady-states and periodic orbits of oscillatory and chaotic electrochemical systems. Two experimental systems were used for the application of the control procedure.…”

Section: Application Of Delayed-feedback Controlmentioning

confidence: 99%

Control of Electrochemical Chaos and Unstable Steady-States

Orlik

2012

Self-Organization in Electrochemical Systems II

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Modern research in the area of deterministic chaotic systems [1] is oriented on acquiring control of this apparently uncontrollable regime. An outline characteristics of the control of chaos was given in Sect. 1.10.3 of volume I. The reader particularly interested in this area can consult, e.g., a recent specialized monograph on that subject [2]. Two landmark papers on the chaos control appeared in 1990. In one of them Ott et al. [3] have described the (OGY) algorithm of converting a chaotic (strange) attractor to any one of a large number of possible attracting time-periodic motions by making only small time-dependent perturbations of an available system parameter. In other words, by applying the appropriate feedback-based strategy one can suppress chaos by maintaining the system's dynamics on a selected, desired periodic phase trajectory. In the second paper, written by Pecora and Carroll [4], it was shown that certain subsystems of nonlinear, chaotic systems can be made to synchronize by linking them with common signals. These theoretical achievements triggered increasing interest also in achieving the stabilization of any unstable states, both in theoretical models and real systems, including electrochemical processes. Several particular algorithms were employed for such strategies based on appropriate feedbacks.For a highly dissipative system (when the strange attractor has a dimension slightly higher than 2), it is convenient to reduce the original OGY approach to a simple map-based

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“…Note that ε(t) vanishes when the system is on the UPO since s(t) = s(t − τ) for all t. This control scheme has been successfully applied to diverse experimental systems such as electronic circuits [28,30,[41][42][43], Taylor-Couette fluid flow [44], an 15 NH 3 laser [45], a strongly driven magnetic system [46], plasma instabilities [47,48], and a chemical reaction [49,50]; see also other chapters of this Handbook. The simplicity of TDAS allows it to be implemented with much less latency than most control schemes.…”

Section: Controlling Fast Systemsmentioning

confidence: 99%