Raphael Nagao

Restoration of rhythmicity in diffusively coupled dynamical networks

Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in)homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks.

Temperature (Over)Compensation in an Oscillatory Surface Reaction

Biological rhythms are regulated by homeostatic mechanisms that assure that physiological clocks function reliably independent of temperature changes in the environment. Temperature compensation, the independence of the oscillatory period on temperature, is known to play a central role in many biological rhythms, but it is rather rare in chemical oscillators. We study the influence of temperature on the oscillatory dynamics during the catalytic oxidation of formic acid on a polycrystalline platinum electrode. The experiments are performed at five temperatures from 5 to 25 °C, and the oscillations are studied under galvanostatic control. Under oscillatory conditions, only non-Arrhenius behavior is observed. Overcompensation with temperature coefficient (q(10), defined as the ratio between the rate constants at temperature T + 10 °C and at T) < 1 is found in most cases, except that temperature compensation with q(10) ≈ 1 predominates at high applied currents. The behavior of the period and the amplitude result from a complex interplay between temperature and applied current or, equivalently, the distance from thermodynamic equilibrium. High, positive apparent activation energies were obtained under voltammetric, nonoscillatory conditions, which implies that the non-Arrhenius behavior observed under oscillatory conditions results from the interplay among reaction steps rather than from a weak temperature dependence of the individual steps.

Temperature effects on the oscillatory electro-oxidation of methanol on platinum

We report in this paper the effect of temperature on the oscillatory electro-oxidation of methanol on polycrystalline platinum in aqueous sulfuric acid media. Potential oscillations were studied under galvanostatic control and at four temperatures ranging from 5 to 35 degrees C. For a given temperature, the departure from thermodynamic equilibrium does not affect the oscillation period and results in a slight increase of the oscillation amplitude. Apparent activation energies were also evaluated in voltammetric and chronoamperometric experiments and were compared to those obtained under oscillatory conditions. In any case, the apparent activation energies values fell into the region between 50 and 70 kJ mol(-1). Specifically under oscillatory conditions an apparent activation energy of 60 +/- 3 kJ mol(-1) and a temperature coefficient q10 of about 2.3 were observed. The present findings extend our recently published report (J. Phys. Chem. A, 2008, 112, 4617) on the temperature effect on the oscillatory electro-oxidation of formic acid. We found that, despite the fact that both studies were carried out under similar conditions, unlike the case of formic acid, only conventional, Arrhenius, dynamics was observed for methanol.

PHASE-SELECTIVE ENTRAINMENT OF NONLINEAR OSCILLATOR ENSEMBLES

The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups into spatiotemporal patterns with multiple phase clusters. The experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.

Mechanistic aspects of the linear stabilization of non-stationary electrochemical oscillations†

The problem of non-stationarity in experimentally recorded time-series is common in many (electro)chemical systems. Underlying this non-stationarity is the slow drift in some uncontrollable parameter, and it occurs in spite of the fact that all controllable parameters are kept constant. Particularly for electrochemical systems, some of us have recently suggested [J. Phys. Chem. C, 144, (2010), 22262-22268] an empirical method to stabilize experimental time-series. The method was exemplified for the electro-oxidation of methanol and different patterns were satisfactorily stabilized. In this paper we further elaborate some mechanistic aspects of this method and test it for the electro-oxidation of formaldehyde, a system that has some resemblance with the electro-oxidation of methanol, but produces a richer dynamics. In terms of the reaction mechanism, we were able to describe the coupling and to separate the surface processes of the two sub-systems: the fast one (or the core-oscillator) and the slow one, responsible for the drift.

The Electro-Oxidation of Ethylene Glycol on Platinum over a Wide pH Range: Oscillations and Temperature Effects

We report a comprehensive study of the electro-oxidation of ethylene glycol (EG) on platinum with emphasis on the effects exerted by the electrolyte pH, the EG concentration, and temperature, under both regular and oscillatory conditions. We extracted and discussed parameters such as voltammetric activity, reaction orders (with respect to [EG]), oscillation’s amplitude, frequency and waveform, and the evolution of the mean electrode potential at six pH values from 0 to 14. In addition, we obtained the apparent activation energies under several different conditions. Overall, we observed that increasing the electrolyte pH results in a discontinuous transition in most properties studied under both voltammetric and oscillatory regimes. As a relevant result in this direction, we found that the increase in the reaction order with pH is mediated by a minimum (~ 0) at pH = 12. Furthermore, the solution pH strongly affects all features investigated, c.f. the considerable increase in the oscillatory frequency and the decrease in the, oscillatory, activation energy as the pH increase. We suggest that adsorbed CO is probably the main surface-blocking species at low pH, and its absence at high pH is likely to be the main reason behind the differences observed. The size of the parameter region investigated and the amount of comparable parameters and properties presented in this study, as well as the discussion that followed illustrate the strategy of combining investigations under conventional and oscillatory regimes of electrocatalytic systems.

Coupled slow and fast surface dynamics in an electrocatalytic oscillator: Model and simulations

The co-existence of disparate time scales is pervasive in many systems. In particular for surface reactions, it has been shown that the long-term evolution of the core oscillator is decisively influenced by slow surface changes, such as progressing deactivation. Here we present an in-depth numerical investigation of the coupled slow and fast surface dynamics in an electrocatalytic oscillator. The model consists of four nonlinear coupled ordinary differential equations, investigated over a wide parameter range. Besides the conventional bifurcation analysis, the system was studied by means of high-resolution period and Lyapunov diagrams. It was observed that the bifurcation diagram changes considerably as the irreversible surface poisoning evolves, and the oscillatory region shrinks. The qualitative dynamics changes accordingly and the chaotic oscillations are dramatically suppressed. Nevertheless, periodic cascades are preserved in a confined region of the resistance vs. voltage diagram. Numerical results are compared to experiments published earlier and the latter reinterpreted. Finally, the comprehensive description of the time-evolution in the period and Lyapunov diagrams suggests further experimental studies correlating the evolution of the systems dynamics with changes of the catalyst structure.

Restoring oscillatory behavior from amplitude death with anti-phase synchronization patterns in networks of electrochemical oscillations

The dynamical behavior of delay-coupled networks of electrochemical reactions is investigated to explore the formation of amplitude death (AD) and the synchronization states in a parameter region around the amplitude death region. It is shown that difference coupling with odd and even numbered ring and random networks can produce the AD phenomenon. Furthermore, this AD can be restored by changing the coupling type from difference to direct coupling. The restored oscillations tend to create synchronization patterns in which neighboring elements are in nearly anti-phase configuration. The ring networks produce frozen and rotating phase waves, while the random network exhibits a complex synchronization pattern with interwoven frozen and propagating phase waves. The experimental results are interpreted with a coupled Stuart-Landau oscillator model. The experimental and theoretical results reveal that AD behavior is a robust feature of delayed coupled networks of chemical units; if an oscillatory behavior is required again, even a small amount of direct coupling could be sufficient to restore the oscillations. The restored nearly anti-phase oscillatory patterns, which, to a certain extent, reflect the symmetry of the network, represent an effective means to overcome the AD phenomenon.

Forcing of Turing patterns in the chlorine dioxide-iodine-malonic acid reaction with strong visible light.

We investigate the sensitivity of Turing patterns in the chlorine dioxide-iodine-malonic acid reaction to illumination by strong white light. Intense illumination results in an increase of [I(-)], in contrast to previous studies, which found only decreased [I(-)] for weak and intermediate intensities of illumination. We propose an expanded mechanism to explain the experimental observations. Both experimental and numerical results suggest that [ClO2] is the key parameter that determines whether the high iodide state is obtained under strong illumination. When strong illumination is applied through a spatially periodic mask with black and white stripes, a dark state with high [I(-)] is produced in the illuminated domain and a light state with low [I(-)] forms in the nonilluminated domain. Depending on the black:white ratio of the mask and its wavelength, Turing patterns can coexist with either the light or the dark state in the nonilluminated domain.

APARATO ELETROQUÍMICO PARA SISTEMA DE AQUISIÇÃO DE DADOS MULTICANAL COM RESOLUÇÃO ESPAÇO-TEMPORAL

Spatiotemporal pattern formation in reaction-transport systems takes place spontaneously when the system is kept far from thermodynamic equilibrium. Targets, reaction fronts, waves, spirals, spots and stripes are some typical examples of selforganized structuring. In electrochemical systems, monitoring spatiotemporal patterns of potential in the solid/liquid interface can be done by the use of equally distributed microprobes located close to the working electrode. However, the physical size of each probe can limit the spatial resolution and alter mass transport properties. In contrast, the direct measurement of discrete electrodes does not suffer from this limitation and allows the accurate manipulation of the spatial coupling through changes in resistors connected to the electric circuit. In this paper, the development of an electrochemical setup for multichannel data acquisition with spatiotemporal resolution is described, especially to monitor low levels of currents usually observed in the electro-oxidation of small organic molecules.