Synchronization using environmental coupling in mercury beating heart oscillators

Synchronization of Belousov-Zhabotinsky oscillators with electrochemical coupling in a spontaneous process

A passive electrochemical coupling approach is proposed to induce spontaneous synchronization between chemical oscillators. The coupling exploits the potential difference between a catalyst redox couple in the Belousov-Zhabotinsky (BZ) reaction, without external feedback, to induce surface reactions that impact the kinetics of the bulk system. The effect of coupling in BZ oscillators under batch condition is characterized using phase synchronization measures. Although the frequency of the oscillators decreases nonlinearly over time, by a factor of 2 or more within 100 cycles, the coupling is strong enough to maintain synchronization. In such a highly drifting system, the Gibbs-Shannon entropy of the cyclic phase difference distribution can be used to quantify the coupling effect. We extend the Oregonator BZ model to account for the drifting natural frequencies in batch condition and for electrochemical coupling, and numerical simulations of the effect of acid concentration on synchronization patterns are in agreement with the experiments. Because of the passive nature of coupling, the proposed coupling scheme can open avenues for designing pattern recognition and neuromorphic computation systems using chemical reactions in a spontaneous process.

Independent-noise provoked spiking, synchronized via coupling

We report experimental and numerical evidence of synchronized spiking phenomena provoked by the interaction of two bidirectionally coupled electrochemical systems subjected to independent stochastic input signals. To this end, the anodic potentials of two such systems were diffusively coupled. The corresponding anodic currents of these systems exhibited excitable fixed point behavior in the vicinity of a homoclinic bifurcation. Following this, the anodic potentials were perturbed by independent noise signals. The invoked oscillatory dynamics are analyzed using normalized variance and cross-correlation coefficient. By systematically varying the coupling strength between the systems and the level of external noise, regions exhibiting synchronized spiking behavior were identified.

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.

Ill-matched timescales in coupled systems can induce oscillation suppression

We explore the behavior of two coupled oscillators, considering combinations of similar and dissimilar oscillators, with their intrinsic dynamics ranging from periodic to chaotic. We first investigate the coupling of two different real-world systems, namely, the chemical mercury beating heart oscillator and the electronic Chua oscillator, with the disparity in the timescales of the constituent oscillators. Here, we are considering a physical situation that is not commonly addressed: the coupling of sub-systems whose characteristic timescales are very different. Our findings indicate that the oscillations in coupled systems are quenched to oscillation death (OD) state, at sufficiently high coupling strength, when there is a large timescale mismatch. In contrast, phase synchronization occurs when their timescales are comparable. In order to further strengthen the concept, we demonstrate this timescale-induced oscillation suppression and phase synchrony through numerical simulations, with the disparity in the timescales serving as a tuning or control parameter. Importantly, oscillation suppression (OD) occurs for a significantly smaller timescale mismatch when the coupled oscillators are chaotic. This suggests that the inherent broad spectrum of timescales underlying chaos aids oscillation suppression, as the temporal complexity of chaotic dynamics lends a natural heterogeneity to the timescales. The diversity of the experimental systems and numerical models we have chosen as a test-bed for the proposed concept lends support to the broad generality of our findings. Last, these results indicate the potential prevention of system failure by small changes in the timescales of the constituent dynamics, suggesting a potent control strategy to stabilize coupled systems to steady states.

Explosive synchronization in temporal networks: A comparative study

We present a comparative study on Explosive Synchronization (ES) in temporal networks consisting of phase oscillators. The temporal nature of the networks is modeled with two configurations: (1) oscillators are allowed to move in a closed two-dimensional box such that they couple with their neighbors and (2) oscillators are static and they randomly switch their coupling partners. Configuration (1) is further studied under two possible scenarios: in the first case, oscillators couple to fixed numbers of neighbors, while, in the other case, they couple to all oscillators lying in their circle of vision. Under these circumstances, we monitor the degrees of temporal networks, velocities, and radius of circle of vision of the oscillators and the probability of forming connections in order to study and compare the critical values of the coupling required to induce ES in the population of phase oscillators.

Oscillatory activity regulation in an ensemble of autonomous mercury beating heart oscillators

Collective behavior of an ensemble of directly or indirectly coupled oscillators can be a function of population density. Experiments using autonomous mercury beating heart (MBH) oscillators coupled through their surroundings are employed, to study the existence of quorum-like (population dependent) phenomena. Two coupling mechanisms are used, namely, static and dynamic coupling. For the static coupling scheme, the transitions of a subset of the coupled oscillators occur from active (oscillatory) to inactive (quiescent) state and vice versa. A continuous variation of collective dynamics was observed as the population of the oscillators increased. For the dynamic coupling scheme, the time for which the coupled oscillators are active changes sharply as the population increases beyond a certain threshold.

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.

Control, synchronization, and enhanced reliability of aperiodic oscillations in the Mercury Beating Heart system

Experiments involving the Mercury Beating Heart (MBH) oscillator, exhibiting irregular (aperiodic) dynamics, are performed. In the first set of experiments, control over irregular dynamics of the MBH oscillator was obtained via a superimposed periodic voltage signal. These irregular (aperiodic) dynamics were recovered once the control was switched off. Subsequently, two MBH oscillators were coupled to attain synchronization of their aperiodic oscillations. Finally, two uncoupled MBH oscillators were subjected, repeatedly, to a common stochastic forcing, resulting in an enhancement of their mutual phase correlation.