Electrical coupling of individual electrocatalytic oscillators.

The catalytic electro-oxidation of some small organic molecules is known to display kinetic instabilities, which reflect on potential and/or current oscillations. Under oscillatory conditions, those systems can be considered electrocatalytic oscillators and, therefore, can be described by their amplitude, frequency, and waveform. Just like mechanical oscillators, the electrocatalytic ones can be coupled and their dynamics can be changed by setting different coupling parameters. In the present work, we study the unidirectional coupling of electrocatalytic oscillators, namely, those comprehending the catalytic electro-oxidation of methanol and formic acid on polycrystalline platinum in acidic media under potentiostatic control. Herein, we explore two different scenarios (the coupling of compositionally identical and non-identical oscillators) and investigate the effects of the master's identity and of the coupling constant on the slave's dynamics. For the master (methanol)-slave (methanol) coupling, the oscillators exhibited phase lag synchronization and complete phase synchronization. On the other hand, for the master (formic acid)-slave (methanol) coupling, the oscillators exhibited complete phase synchronization with phase-locking with a 2:3 ratio, complete phase synchronization with phase-locking with a 1:2 ratio, phase lag synchronization, and complete phase synchronization. The obtained results suggest that both the master's identity and the coupling constant (sign and magnitude) are parameters that play an important role on the coupled systems, in such a way that even for completely different systems, synchronization could emerge by setting a suitable coupling constant. To the best of our knowledge, this is the first report concerning the electrical coupling of hidden N-shaped-negative differential resistance type systems.

An alternate approach to simulate the dynamics of perturbed liquid drops.

Liquid drops when subjected to external periodic perturbations can execute polygonal oscillations. In this work, a simple model is presented that demonstrates these oscillations and their characteristic properties. The model consists of a spring-mass network such that masses are analogous to liquid molecules and the springs correspond to intermolecular links. Neo-Hookean springs are considered to represent these intermolecular links. The restoring force of a neo-Hookean spring depends nonlinearly on its length such that the force of a compressed spring is much higher than the force of the spring elongated by the same amount. This is analogous to the incompressibility of liquids, making these springs suitable to simulate the polygonal oscillations. It is shown that this spring-mass network can imitate most of the characteristic features of experimentally reported polygonal oscillations. Additionally, it is shown that the network can execute certain dynamics, which so far have not been observed in a perturbed liquid drop. The characteristics of dynamics that are observed in the perturbed network are polygonal oscillations, rotation of network, numerical relations (rational and irrational) between the frequencies of polygonal oscillations and the forcing signal, and that the shape of the polygons depends on the parameters of perturbation.

Electrical resonance of Amphotericin B channel activity in lipidic membranes.

In our previous work [J. Membrane Biol. 237, 31 (2010)], we showed the dependence of the time average conductance of Nystatin channels as a function of the applied potential. Specifically, it was observed that greater potential induced enhanced channel activity. This indicates that the supramolecular structure could be stabilized by a large field, possibly by giving a preferential orientation to the monomers. In the present work, we entertain the notion that the process of pore formation in the lipidic membranes has an underlying deterministic component. To verify this hypothesis, experiments were performed under potentio-dynamic conditions, i.e., a square train of pulses of different frequencies (0.05-2 Hz) were applied to a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine membrane having 30 mol. % cholesterol and the presence of 35 µM Amphotericin B. An emergence of a resonant frequency, in the present experiments, is tantamount to observing fingerprints of determinism in the activity of these channels in lipidic membranes.

Tracking stochastic resonance curves using an assisted reference model.

The optimal noise amplitude for Stochastic Resonance (SR) is located employing an Artificial Neural Network (ANN) reference model with a nonlinear predictive capability. A modified Kalman Filter (KF) was coupled to this reference model in order to compensate for semi-quantitative forecast errors. Three manifestations of stochastic resonance, namely, Periodic Stochastic Resonance (PSR), Aperiodic Stochastic Resonance (ASR), and finally Coherence Resonance (CR) were considered. Using noise amplitude as the control parameter, for the case of PSR and ASR, the cross-correlation curve between the sub-threshold input signal and the system response is tracked. However, using the same parameter the Normalized Variance curve is tracked for the case of CR. The goal of the present work is to track these curves and converge to their respective extremal points. The ANN reference model strategy captures and subsequently predicts the nonlinear features of the model system while the KF compensates for the perturbations inherent to the superimposed noise. This technique, implemented in the FitzHugh-Nagumo model, enabled us to track the resonance curves and eventually locate their optimal (extremal) values. This would yield the optimal value of noise for the three manifestations of the SR phenomena.

Endogenous CO2 may inhibit bacterial growth and induce virulence gene expression in enteropathogenic Escherichia coli.

Analysis of the growth kinetics of enteropathogenic Escherichia coli (EPEC) revealed that growth was directly proportional to the ratio between the exposed surface area and the liquid culture volume (SA/V). It was hypothesized that this bacterial behavior was caused by the accumulation of an endogenous volatile growth inhibitor metabolite whose escape from the medium directly depended on the SA/V. The results of this work support the theory that an inhibitor is produced and indicate that it is CO(2). We also report that concomitant to the accumulation of CO(2), there is secretion of the virulence-related EspB and EspC proteins from EPEC. We therefore postulate that endogenous CO(2) may have an effect on both bacterial growth and virulence.

Effect of the volume-to-surface ratio of cultures on Escherichia coli growth: an experimental and theoretical analysis.

The growth dynamics of bacterial populations are usually represented by the classical S-shaped profiles composed of lag, exponential and stationary growth phases. Although exceptions to this classical behavior occur, they are normally produced under non-standard conditions such as supply of two carbohydrates as sole carbon source. However, we here report variations in the classic S-shaped growth profiles of Escherichia coli under standard culturing conditions; explicitly, we found growth during transition to the stationary phase wherein the bacterial growth rate inversely depended on the volume-to-surface ratio of cultures (V/S); the reasons for this behavior were experimentally explored. To complement our experimental analysis, a theoretical model that rationalizes the bacterial response was developed; simulations based on the developed model essentially reproduced experimental growth curves. We consequently conclude that the effect of V/S on E. coli growth reflects an interplay between auto-catalytic bacterial growth, bacterial growth auto-inhibition, and, the relief of that inhibition.

Chaotic synchronization under unidirectional coupling: numerics and experiments.

Synchronization for a pair of chaotic oscillators is studied both numerically and experimentally. The two oscillators are coupled unidirectionally, namely, in the master slave configuration. When the coupling strength is systematically varied, different regimes of chaotic synchronization such as no, phase, lag and complete are identified. The existence of natural lag synchronization for unidirectional coupling is by virtue of a small parameter mismatch between the master and the slave oscillators. Numerical calculations are carried out in the Rössler model whereas the experiments are performed using a pair of electrochemical oscillators.

Comparing the coherence resonance curves invoked by different types of forcing.

We study the different coherence resonance (CR) phenomena induced when an excitable FitzHugh-Nagumo-type system is forced using diverse deterministic and/or stochastic time series. The possible implications of this comparative study involving these different CR's are also discussed. The main result of the present work suggests that for appropriate forcing and system parameters the generated CR curves reflect the correlations of the superimposed time series.

Experimental observation of different types of chaotic synchronization in an electrochemical cell.

Chaotic synchronization for a pair of electrochemical oscillators is studied experimentally. The underlying bidirectional coupling between the two oscillators is achieved by immersing the two anodes in a common electrolytic solution. The horizontal distance between these two electrodes determines the strength of the coupling constant. On monotonically decreasing the distance between the two anodes, different domains of chaotic synchronization, namely, no, phase, lag, and complete synchronization, are identified. Furthermore, dynamics from the different transition intervals are also characterized.

Stochastic resonance of electrochemical aperiodic spike trains.

Aperiodic stochastic resonance in an electrochemical system with excitable dynamics is characterized in experiments and simulations. Two different spike trains, one with stochastic and the other with chaotic interspike intervals, are imposed on the system as subthreshold aperiodic signals. Information transmission is quantified by the cross correlation between the subthreshold input signal and the noise induced system response. A maximum is exhibited in the input-output correlation as a function of the noise amplitude. Numerical simulations with an electrochemical model are in excellent agreement with the experimental observations.

Parameter space reduction criteria to search for synchronization domains in coupled discrete systems.

Based on analytical considerations, we introduce criteria that enable us to encapsulate the parameter domains for which chaotic synchronization in linearly coupled map systems may be attained. Our aim is to provide means to readily determine parameter regions which preclude synchronization. This results in a significant reduction of parameter space that one needs to explore. Our findings hold for both identical and quasi-identical (small parameter mismatch) maps subjected to unidirectional and bidirectional coupling. As a testing ground we present numerical calculations for the logistic and cubic maps which validate the predictive capability of our approach. Our main contribution relies on the applicability of one of our criteria to experimental situations. Since in real life it is almost impossible to construct two truly identical systems, the results for quasi-identical maps are of particular relevance.

Effects of noise near a homoclinic bifurcation in an electrochemical system.

The interaction of external noise with an electrochemical oscillator (anodic dissolution of iron) has been studied experimentally on both sides of the homoclinic bifurcation. In the oscillatory regime the regularity of the limit cycle behavior was destroyed with increasing noise amplitude until no periodicity was observable any more. In contrast, the response of the excitable state (fixed point regime) became more regular at intermediate noise levels.

Experimental evidence of coexisting periodic stochastic resonance and coherence resonance phenomena.

We report evidence of coexisting period stochastic resonance (PSR) and coherence resonance (CR) phenomena in an electrochemical cell. The anodic voltage (V) in the cell is chosen such that the anodic current (I) exhibits excitable fixed point behavior. Subsequently, the anodic voltage is modulated by an external perturbation that is a composite of a subthreshold periodic pulse signal and Gaussian white noise (GWN). As the amplitude of the GWN is increased, the regularity of the invoked dynamics is analyzed using normalized variance curve. The calculated resonance curve shows a double minima, implying the existence of two optimum noise levels where enhanced regularity of the induced spike sequence is detected. Numerical simulations corroborate experimental findings.

Tracking fixed-point dynamics in an electrochemical system using delayed-feedback control.

We report numerical and experimental results indicating successful tracking of stabilized fixed points solutions in an electrochemical system. By applying a continuous delayed-feedback technique, periodic oscillations are suppressed via stabilization of a steady-state fixed point. Subsequently, using a simple continuation method involving an update term, this stabilized fixed point is tracked through the bifurcation diagram as a system parameter is slowly varied. Under the influence of this tracking protocol, inception of oscillatory dynamics is precluded over large parameter domains and through bifurcations.

Resonant forcing of a silent Hodgkin-Huxley neuron.

Dynamical behavior of a silent Hodgkin-Huxley neuron subjected to external periodic perturbations is investigated. Induced dynamics for this forced system, exhibit nonlinear resonance with respect to the forcing frequency. Within the U-shaped resonance curve, both regular (phase locked) and irregular spike sequences are invoked. For appropriate tuning frequencies, this simple system generates spike trains recordings similar to ones observed in actual experiments.

Resonances via deterministic and stochastic perturbations: a comparative study.

We study periodic and coherence resonances invoked by aperiodic yet deterministic perturbations. Chaotic perturbations with varying levels of intrinsic correlations are superimposed parametrically on an excitable chemical model. This enables us to analyze the system response and characterize the induced resonances as a function of correlation in the perturbing signal. Using standard measures such as normalized variance and normalized number of peaks, dynamics for different deterministic signals are quantified and eventually compared to resonances invoked via stochastic perturbations.

Suppressing spatiotemporal disorder via local perturbations in an electrochemical cell.

We report experimental results depicting suppression of complex spatiotemporal dynamics under the influence of local periodic stimulations. In an experimental electrochemical system, applying a continuous forcing signal to one of the sites in an array of eight coupled oscillators, the naturally complex behavior of the remaining seven electrodes can be converted to periodic responses. The oscillations remain periodic as long as the forcing is active and revert back to exhibiting chaotic dynamics after the control is switched off. These results can also be interpreted as experimental realization of "phase-synchronization" induced via local driving in an extended system. A possible relevance to the experimentally observed calcium wave patterns is pointed out.

Birhythmicity induced by perturbing an oscillating electrochemical system.

We describe the generation of new limit cycles in electrochemical systems under the influence of external periodic perturbations. For certain specific parameters of a nonharmonic forcing function, two coexisting periodic orbits can be generated from a single limit cycle observed in the unperturbed dynamics. This inception of birhythmicity (bistability) is observed in both simulations and actual experiments involving potentiostatic electrodissolution of copper in an acetate buffer.

Maintenance of transient chaos using a neural-network-assisted feedback control.

A stable period-3 orbit in the parametric vicinity of a chaotic attractor is destabilized using two distinct feedback strategies. This results in the inception and subsequent maintenance of the otherwise short-lived chaotic transients. Both the techniques employed are based on the exclusion of trajectories from the near vicinity of the open loop stable period-3 attractor; the first relies on the traditional proportional feedback method while the second one includes a predictive term enabling delimitation of exclusion zones for the system dynamics. The implementation of these strategies involves construction of appropriate reference models in the form of an artificial-neural-network approximator.

Controlling spatiotemporal chemical chaos using delayed feedback.

Control of chemical chaos in a spatially extended system mimicking CO oxidation on a Pt(110) single-crystal surface is achieved using delayed feedback techniques. For appropriate parameter values the uncontrolled model system exhibits both amplitude and phase turbulence. Superimposing a delayed feedback on the natural dynamics, suppression of spatiotemporal complexity is attained via stabilization of ordered states consisting of stable patterns.