Excitability in a closed stirred Belousov—Zhabotinskii system

Spontaneous Symmetry Breaking: The Case of Crazy Clock and Beyond

In this work, we describe the crazy-clock phenomenon involving the state I (low iodide and iodine concentration) to state II (high iodide and iodine concentration with new iodine phase) transition after a Briggs–Rauscher (BR) oscillatory process. While the BR crazy-clock phenomenon is known, this is the first time that crazy-clock behavior is linked and explained with the symmetry-breaking phenomenon, highlighting the entire process in a novel way. The presented phenomenon has been thoroughly investigated by running more than 60 experiments, and evaluated by using statistical cluster K-means analysis. The mixing rate, as well as the magnetic bar shape and dimensions, have a strong influence on the transition appearance. Although the transition for both mixing and no-mixing conditions are taking place completely randomly, by using statistical cluster analysis we obtain different numbers of clusters (showing the time-domains where the transition is more likely to occur). In the case of stirring, clusters are more compact and separated, revealed new hidden details regarding the chemical dynamics of nonlinear processes. The significance of the presented results is beyond oscillatory reaction kinetics since the described example belongs to the small class of chemical systems that shows intrinsic randomness in their response and it might be considered as a real example of a classical liquid random number generator.

Pulse propagation in a 1D array of excitable semiconductor lasers

Nonlinear pulse propagation is a major feature in continuously extended excitable systems. The persistence of this phenomenon in coupled excitable systems is expected. Here, we investigate theoretically the propagation of nonlinear pulses in a 1D array of evanescently coupled excitable semiconductor lasers. We show that the propagation of pulses is characterized by a hopping dynamics. The average pulse speed and bifurcation diagram are characterized as a function of the coupling strength between the lasers. Several instabilities are analyzed such as the onset and disappearance of pulse propagation and a spontaneous breaking of the translation symmetry. The pulse propagation modes evidenced are specific to the discrete nature of the 1D array of excitable lasers.

Mechanism and Phenomenology of an Oscillating Chemical Reaction

Chemical reactions, which are far from equilibrium, are capable of displaying oscillations in species concentrations and hence in colour, electrode potential, pH and/or temperature. The oscillations arise from the interplay between positive and negative kinetic feedback. Mechanisms for such reactions are presented, along with the rich phenomenology that these systems exhibit, from complex oscillations and chemical waves, to stationary concentration patterns. This review will focus on the Belousov-Zhabotinksy reaction but reference to other reactions will be made where appropriate.

Excitability in ramped systems: the compost-bomb instability

The paper studies a novel excitability type where a large excitable response appears when a system’s parameter is varied gradually, or ramped, above some critical rate. This occurs even though there is a (unique) stable quiescent state for any fixed setting of the ramped parameter. We give a necessary and a sufficient condition for the existence of a critical ramping rate in a general class of slow–fast systems with folded slow (critical) manifold. Additionally, we derive an analytical condition for the critical rate by relating the excitability threshold to a canard trajectory through a folded saddle singularity. The general framework is used to explain a potential climate tipping point termed the ‘compost-bomb instability’—an explosive release of soil carbon from peatlands into the atmosphere occurs above some critical rate of global warming even though there is a unique asymptotically stable soil carbon equilibrium for any fixed atmospheric temperature.

Stirring-Controlled Bifurcations in the 1,4-Cyclohexanedione−Bromate Reaction

We report the experimental observation that stirring in a closed 1,4-cyclohexanedione-bromate reaction can induce transitions not only between oscillatory and nonoscillatory states but also between simple and period-doubled oscillations. Notably, the transition from simple to complex oscillations occurs as a result of increasing stirring rate. When illumination was employed to characterize the importance of microfluctuations of concentrations, the threshold stirring rate for inducing a bifurcation was found to increase proportionally to the intensity of the applied light. Numerical simulations with an existing model illustrate that the experimental phenomena could be qualitatively reproduced by considering effects of mixing on diffusion-limited radical reactions, namely, the disproportion reaction of hydroquinone radicals.

Transient complex oscillations in a closed chemical system with coupled autocatalysis

In this study, hydroquinone was introduced to the classic Belousov-Zhabotinsky (BZ) reaction to build up coupled autocatalytic feedbacks. Various complex dynamical behaviors including successive period-adding bifurcations, irregular oscillations, and frequency modulations were observed in the coupled reaction system. Not only the complexity of oscillations but also the time period during which complex oscillations persist were found to depend greatly on the initial concentration of hydroquinone, which was expected to manifest the coupling strength in the studied system. Dependence of the observed transient complex oscillations on concentrations of ferroin, sulfuric acid, bromate, and malonic acid was also characterized systematically. Numerical simulations with a modified BZ model via incorporating reactions involving hydroquinone and products of hydroquinone qualitatively reproduced the influence of hydroquinone seen in experiments.

Homogenization induced by chaotic mixing and diffusion in an oscillatory chemical reaction

A model for an imperfectly mixed batch reactor with the chlorine dioxide-iodine-malonic acid (CDIMA) reaction, with the mixing being modelled by chaotic advection, is considered. The reactor is assumed to be operating in oscillatory mode and the way in which an initial spatial perturbation becomes homogenized is examined. When the kinetics are such that the only stable homogeneous state is oscillatory then the perturbation is always entrained into these oscillations. The rate at which this occurs is relatively insensitive to the chemical effects, measured by the Damköhler number, and is comparable to the rate of homogenization of a passive contaminant. When both steady and oscillatory states are stable, spatially homogeneous states, two possibilities can occur. For the smaller Damköhler numbers, a localized perturbation at the steady state is homogenized within the background oscillations. For larger Damköhler numbers, regions of both oscillatory and steady behavior can co-exist for relatively long times before the system collapses to having the steady state everywhere. An interpretation of this behavior is provided by the one-dimensional Lagrangian filament model, which is analyzed in detail.

Deterministic chaos in the Belousov-Zhabotinsky reaction: Experiments and simulations

An account of the experimental discovery of complex dynamical behavior in the continuous-flow, stirred tank reactor (CSTR) Belousov-Zhabotinsky (BZ) reaction, as well as numerical simulations based on the BZ chemistry are given. The most recent four- and three-variable models that are deduced from the well-accepted, updated chemical mechanism of the BZ reaction and which exhibit robust chaotic states are summarized. Chaos has been observed in experiments and simulations embedded in the regions of complexities at both low and high flow rates. The deterministic nature of the observed aperiodicities at low flow rates is unequivocally established. However, controversy still remains in the interpretation of certain aperiodicities observed at high flow rates.

NADH substrate inhibition and enhanced thermal stability of higher plant nitrate reductase immobilized via a monoclonal antibody

The molecular basis of light-induced circadian rhythms of higher plant NADH:nitrate reductase (EC 1.6.6.1) activity is presently not understood. We have investigated whether the regulatory properties of NADH:nitrate reductase would allow oscillatory or related dynamic behavior. We report here the first example of NADH substrate inhibition of higher plant nitrate reductase in solution and for an immobilized enzyme using a novel immobilization technique with a monoclonal antibody. According to current theories on chemical oscillatory reactions, substrate inhibition will allow bistable and oscillatory behavior when the substrate-enzyme reaction is carried out in an open system. We also found a significant enhanced thermal stability of the immobilized enzyme.