M. Rivera

Suppression and generation of rhythms in conjugately coupled nonlinear systems

We explore two diametrically opposite phenomena provoked by conjugate coupling in nonlinear systems. The first effect, known as amplitude death, is observed when the two uncoupled systems are located in the oscillatory regime. In the presence of an appropriate coupling term the oscillatory behavior in both the systems vanishes. This amplitude death is found to persist for nonidentical oscillators, exhibiting different dynamics. In contrast, when the two uncoupled systems are located in the quiescent domain (fixed point behavior), suitable conjugate coupling seems to be capable of generating rhythms in the two systems. Similar to its amplitude death counterpart, induction of rhythms/oscillations is also observed for nonidentical systems. We demonstrate the phenomenon of amplitude death and oscillation generation by numerically studying two different systems, namely, an electrochemical corrosion model and the Hodgkin-Huxley model for neuronal spiking.

Altering oscillatory dynamics of an electrochemical system using external forcing

Abstract We report results (numerical and experimental) indicating control of observed oscillatory dynamics in an electrochemical system under the influence of superimposed sinusoidal forcing. By varying the frequency and amplitude of the external forcing (control parameters) not only were the chaotic dynamics converted to periodic states (controlling chaos via entrainment), but the period-1 (P1) behavior could also be transformed to oscillatory dynamics of higher periodicity (for example: P2). Therefore for appropriate values of control constants and nature of the unperturbed (periodic and/or chaotic) dynamics, a final state of either lower (chaos→P1) or higher complexity (P1→P2) can be attained. Since no prior information regarding the system dynamics is required for implementation of the forcing control it is thus relevant for application to real systems.

Interaction of noise with excitable dynamics

In this paper, the interaction of noise with excitable dynamics of a three-electrode electrochemical cell is examined. Different scenarios involving both external and internal noise sources are considered. In the case of external noise, aperiodic stochastic resonance and regulation of the noise-induced spiking behaviour are investigated. In the case of internal noise, the interaction of intrinsic electrochemical noise with autonomous nonlinear dynamics is studied. The amplitude of this internal noise, determined by the concentration of chloride ions, is monotonically increased and the provoked dynamics are analysed. Our results indicate that internal noise, similar to its external counterpart, is able to induce regularity in the system response.

Synchronization phenomena for a pair of locally coupled chaotic electrochemical oscillators: a survey.

Chaotic synchronization of two locally coupled electrochemical oscillators is studied numerically. Both bidirectional and unidirectional couplings are considered. For both these coupling scenarios, varying the characteristics of the coupling terms (functional form and/or strength) reveals a wide variety of synchronization phenomena. Standard diagnostic tests are performed to verify and classify the different types of synchronizations observed.

Extensive study of shape and surface structure formation in the mercury beating heart system.

A phenomenological study of the mercury beating heart system in a three electrode electrochemical cell configuration forced with a harmonic perturbation is presented. The system is controlled via a potentiostat, where the mercury drop is electrically connected to a platinum wire and acts as the working electrode. This configuration exhibits geometrical shapes and complex surface structures when a harmonic signal is superimposed to the working electrode potential. This study involves a wide range of frequencies and amplitudes of the forcing signal. Differents levels of structure complexity are observed as a function of the parameters of the applied perturbation. At certain amplitudes and frequencies, rotational behavior is also observed.

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.

Inducing rotational motion in the mercury beating heart system

In this paper, we report experimental results showing the generation of rotational motion in a non-autonomous Mercury Beating Heart system. Using an electrochemical cell under potentiostatic conditions, a traveling chemomechanical wave can be created on the periphery of the surface of a mercury drop, placed on a concave glass surface, and completely immersed in an acidic media. Due to the spherical geometry of the container, this chemomechanical wave deforms continuously the surface of the drop to induce a variety of rotatory dynamics with different topological structures. In the present study, the applied potential was systematically varied to observe the different dynamical structures. Since the time series of the generated current does not provide useful information, the corresponding image analysis of the bidimensional projection of the surface of the drop was performed in order to verify the existence of the traveling waves.

Kuramoto transition in an ensemble of mercury beating heart systems

We have studied, experimentally, the collective behavior of the electrically coupled autonomous Mercury Beating Heart (MBH) systems exhibiting the breathing mode, by varying both the coupling strength and the population size (from N = 3 to N = 16). For a fixed N, the electrical and the mechanical activities of the MBH systems achieve complete synchronization at different coupling strengths. The electrical activity of each MBH system is measured by the corresponding electrode potential (Ei = Vi). Additionally, the mechanical activity of each MBH oscillator is visually observed (snapshots and video clips). Subsequently, this activity is quantified by calculating the temporal variation in the area (Ai) of the Hg drop. As a result, the synchronization of the electrical (Ei = Vi) and the mechanical (Ai) activities can be measured. The extent of synchronization was quantified by employing the order parameter (r). Our experimental results are found to be in agreement with the Kuramoto theory.

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.

Controlling complexity using forcing: simulations and experiments

We report the successful manipulation of non-linear dynamics using external forcing. In the case of temporal systems, a model system involving ordinary differential equations (odes) was used for simulations. Experiments were carried out in a single anode electrochemical cell. Numerical and experimental results indicate that under the influence of external forcing, control of complexity and a change in periodicity of the autonomous dynamics can be achieved. A natural extension of this work involves analyzing the effects of global and local forcing on complex spatio-temporal behavior. A numerical model involving partial differential equations (pdes) was used for simulating the dynamics of this extended system. An electrochemical cell involving multiple anodes was used for the corresponding experiments. In simulations and in experiments, suppression of spatio-temporal complexity is observed for the two forcing (global and local) methods.