Abrupt and gradual onset of synchronized oscillations due to dynamical quorum sensing in the single-cathode multi-anode nickel electrodissolution system.

The nonlinear dynamics of an oscillatory Ni electrodissolution-hydrogen ion reduction system are explored in a multi-electrode anode-single cathode system. A mathematical analysis of the charge balance equations reveals that the coupling scheme is similar to dynamical quorum sensing, where the number of anode wires affects a parameter related to the population density. In a parameter region where the large population exhibits stationary behavior, with sufficiently strong coupling (with small individual resistances attached to the anode wires), synchronized oscillations emerge abruptly with decreasing the number of anodes. Therefore, an "inverse" dynamical quorum sensing takes place. With weak coupling the transition is gradual. The experiments are supported by numerical simulation of a kinetic model of the process. The results thus show that the description of nontrivial cathode-anode interactions in the form of dynamical quorum sensing provides an efficient way of analyzing the dynamical response of complex, interacting electrochemical reactions.

Delayed feedback induced multirhythmicity in the oscillatory electrodissolution of copper.

Occurrence of bi- and trirhythmicities (coexistence of two or three stable limit cycles, respectively, with distinctly different periods) has been studied experimentally by applying delayed feedback control to the copper-phosphoric acid electrochemical system oscillating close to a Hopf bifurcation point under potentiostatic condition. The oscillating electrode potential is delayed by τ and the difference between the present and delayed values is fed back to the circuit potential with a feedback gain K. The experiments were performed by determining the period of current oscillations T as a function of (both increasing and decreasing) τ at several fixed values of K. With small delay times, the period exhibits a sinusoidal type dependence on τ. However, with relatively large delays (typically τ ≫ T) for each feedback gain K, there exists a critical delay τcrit above which birhythmicity emerges. The experiments show that for weak feedback, Kτcrit is approximately constant. At very large delays, the dynamics becomes even more complex, and trirhythmicity could be observed. Results of numerical simulations based on a general kinetic model for metal electrodissolution were consistent with the experimental observations. The experimental and numerical results are also interpreted by using a phase model; the model parameters can be obtained from experimental data measured at small delay times. Analytical solutions to the phase model quantitatively predict the parameter regions for the appearance of birhythmicity in the experiments, and explain the almost constant value of Kτcrit for weak feedback.

Scaling relationship for oscillating electrochemical systems: dependence of phase diagram on electrode size and rotation rate.

Dynamics of oscillations in electrochemical systems are affected by both chemical and physical properties of the systems. Chemical properties include the type of electrochemical reaction, the electrode material, the composition of the electrolyte, etc., while physical properties include the solution resistance, the cell constant, the electrode size, the rotation rate, the external resistance, etc. Earlier, we proposed the application of cell-geometry-independent phase-diagrams to characterize the oscillatory regions in the electrode potential vs. external resistance parameter plane. In this report, we investigate how this type of phase diagram changes with the surface area (electrode radius) and the rotation rate of an electrode. Based on linear stability analysis of a general, two-variable model for negative-differential resistance (NDR) type electrochemical oscillators we propose a scaling relationship. It predicts that all scaled data points derived from the critical values of parameters (resistance and potential) characterizing the onset of oscillations should fall - independently of the size of the electrode and the rotation rate - on a single plot. The analytical predictions are tested in both numerical simulations and experiments with copper electrodissolution in phosphoric acid.

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

Experimental results are presented on successful application of delayed-feedback control algorithms for tracking unstable steady states and periodic orbits of electrochemical dissolution systems. Time-delay autosynchronization and delay optimization with a descent gradient method were applied for stationary states and periodic orbits, respectively. These tracking algorithms are utilized in constructing experimental bifurcation diagrams of the studied electrochemical systems in which Hopf, saddle-node, saddle-loop, and period-doubling bifurcations take place.

Experimental strategy for characterization of essential dynamical variables in oscillatory systems: effect of double-layer capacitance on the stability of electrochemical oscillators.

An experimentally accessible algorithm for changing the time scale associated with a dynamical variable is proposed. In general, a differential controller can be applied to (a) identify the essential species in oscillatory systems and (b) explore their role in the feedback loops. Here, we report on classifying electrochemical oscillators by changing the time scale over which the electrode potential varies; the type of different electrochemical oscillators is identified based on whether the controlled modification of pseudo-capacitance induces or suppresses current oscillations.

Transverse coupling of chemical waves.

The transverse coupling of chemical waves is investigated using a model scheme for excitable media. Chemical waves supported on the surfaces of a semipermeable membrane couple via diffusion through the membrane, resulting in new types of spatiotemporal behavior. The model studies show that spontaneous wave sources may develop from interacting planar waves, giving rise to a complex sequence of patterns accessible only by perturbation. Coupled circular waves result in the spontaneous formation of spiral waves, which subsequently develop patterns in distinct domains with characteristic features. The long time entrainment behavior of coupled spiral waves reveals regions of 1:2 phase locking.