P. Parmananda

Noise-invoked resonances near a homoclinic bifurcation in the glow discharge plasma

Stochastic resonance (SR) and coherence resonance (CR) have been studied experimentally in discharge plasmas close to a homoclinic bifurcation. For the SR phenomenon, it is observed that a superimposed subthreshold periodic signal can be recovered via stochastic modulations of the discharge voltage. Furthermore, it is realized that even in the absence of a subthreshold deterministic signal, the system dynamics can be recovered and optimized using noise. This effect is defined as CR in the literature. In the present experiments, induction of SR and CR is quantified using the absolute mean difference and normalized variance techniques, respectively.

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.

Noise-Induced Enantioselection in Chiral Autocatalysis

Noise added to a chirally autocatalytic model system is usually known to cause mirror-symmetry breaking with statistically equal distributions for the two product enantiomers. We show that if such a system is asymmetrically perturbed by means of a very small undetectable bias in the racemization equilibrium between the two enantiomers, adding Gaussian white noise can lead to an efficient enantioselection. Consequently, within a certain range of the noise amplitude, symmetry breaking gives rise to an entirely biased statistical distribution in favor of one of the enantiomers. In contrast, racemic results will be obtained for the corresponding deterministic case (in the absence of noise). Thus, added noise plays a constructive role by directing the chiral system into a specific enantiomeric direction while being influenced only by a subthreshold asymmetric input. This effect could be of conceptual interest for the impact of weak asymmetric fields on nonlinear chemical reactions.

Potential-dependent topological modes in the mercury beating heart system.

We study the dynamics of the mercury beating heart (MBH) system in an acidic solution in the absence of a strong oxidant. Furthermore, the system is subjected to an external square wave potential. It was observed that different shapes (circular, elliptical, triangular, and multilobed stars) of the mercury drop could be stabilized as the frequency of the external potential and the volume of the mercury were varied. The redox potential time series for this forced MBH system, corresponding to the different stabilized topological configurations, were also recorded, and their power spectra were analyzed. The obtained results, involving the different topological modes, were fairly reproducible and sustainable. A possible oxidation-reduction mechanism for these experimental observations is provided.

Synchronization in Autonomous Mercury Beating Heart Systems

The ability of the mercury beating heart (MBH) system to exhibit sustained mechanical and electrochemical activities simultaneously without any external agent (fluctuating or constant), has attracted researchers for decades. The interplay of these activities could mimic the biological phenomena such as a pulsating heart that occurs due to the coupled tissues exhibiting mechanical as well as electrical dynamics. In the present work, we have studied experimentally the dynamics of electrically coupled two and three autonomous MBH systems. A dynamical triangular (heart) shape, in the traditional watch glass geometry, has been chosen for the experiments. It is found that the redox potentials (electrical behavior) of the quasi-identical (due to the inherent heterogeneities in the setup) MBH systems get synchronized at the intermediate coupling strengths whereas coherence in their mechanical activities occur only at large coupling strengths. To the best of our knowledge, this synchronization phenomenon involving two distinct activities (electrical and mechanical) and different coupling thresholds has not been reported, so far. The coherent mechanical activities means the simultaneous occurrence of compressions and expansions in the coupled Hg drops, which are shown using snapshots. In addition to this, the redox time series have also been provided to demonstrate the synchronization in the electrical behavior of MBH systems. Moreover, a mathematical framework considering only electrical and mechanical components of the MBH systems is presented to validate the experimental findings that the strong synchrony in the redox potentials of the MBH systems is a prerequisite for the synchrony in their mechanical activities.

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.

Coexisting synchronous and asynchronous states in locally coupled array of oscillators by partial self-feedback control.

We report the emergence of coexisting synchronous and asynchronous subpopulations of oscillators in one dimensional arrays of identical oscillators by applying a self-feedback control. When a self-feedback is applied to a subpopulation of the array, similar to chimera states, it splits into two/more sub-subpopulations coexisting in coherent and incoherent states for a range of self-feedback strength. By tuning the coupling between the nearest neighbors and the amount of self-feedback in the perturbed subpopulation, the size of the coherent and the incoherent sub-subpopulations in the array can be controlled, although the exact size of them is unpredictable. We present numerical evidence using the Landau-Stuart system and the Kuramoto-Sakaguchi phase model.

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.