Asymmetric coupling stabilizes the out-of-phase mode: experimental evidence in the Belousov—Zhabotinsky reaction

Coexistence of oscillatory and reduced states on a spherical field controlled by electrical potential

The Belousov-Zhabotinsky (BZ) reaction was investigated to elucidate features of oscillations depending on the applied electrical potential, E. A cation-exchange resin bead loaded with the catalyst of the BZ reaction was placed on a platinum plate as a working electrode and then E was applied. We found that global oscillations (GO) and a reduced state coexisted on the bead at a negative value of E and that the source point of GO changed depending on E. The thickness of the reduced state was determined by a yellow colored region which corresponded to the distribution of Br₂. The present studies suggest that the distribution of the inhibitor, Br^-, which is produced from Br₂, plays an important role in the existence of the reduced state and GO, and the source point of GO.

Chemical micro-oscillators based on the Belousov–Zhabotinsky reaction

The results of studies on the development of micro-oscillators (MOs) based on the Belousov –Zhabotinsky (BZ) oscillatory chemical reaction are integrated and systematized. The mechanisms of the BZ reaction and the methods of immobilization of the catalyst of the BZ reaction in micro-volumes are briefly discussed. Methods for creating BZ MOs based on water microdroplets in the oil phase and organic and inorganic polymer microspheres are considered. Methods of control and management of the dynamics of BZ MO networks are described, including methods of MO synchronization. The prospects for the design of neural networks of MOs with intelligent-like behaviour are outlined. Such networks present a new area of nonlinear chemistry, including, in particular, the creation of a chemical ‘computer’.

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Aging in global networks with competing attractive-Repulsive interaction

We study the dynamical inactivity of the global network of identical oscillators in the presence of mixed attractive and repulsive coupling. We consider that the oscillators are a priori in all to all attractive coupling and then upon increasing the number of oscillators interacting via repulsive interaction, the whole network attains a steady state at a critical fraction of repulsive nodes, p_c. The macroscopic inactivity of the network is found to follow a typical aging transition due to competition between attractive-repulsive interactions. The analytical expression connecting the coupling strength and p_c is deduced and corroborated with numerical outcomes. We also study the influence of asymmetry in the attractive-repulsive interaction, which leads to symmetry breaking. We detect chimera-like and mixed states for a certain ratio of coupling strengths. We have verified sequential and random modes to choose the repulsive nodes and found that the results are in agreement. The paradigmatic networks with diverse dynamics, viz., limit cycle (Stuart-Landau), chaos (Rössler), and bursting (Hindmarsh-Rose neuron), are analyzed.

Competition between global feedback and diffusion in coupled Belousov-Zhabotinsky oscillators

The Belousov-Zhabotinsky (BZ) reaction is a famous experimental model for chemical oscillatory reaction and pattern formation. We herein study a diffusive coupled system of two oscillators with global feedback using the photosensitive BZ reaction both experimentally and theoretically. The coupled oscillator showed in-phase and antiphase oscillations depending on the strength of diffusive coupling and light feedback. Moreover, we analyzed our model to locate the bifurcational origin and found the reconnection of the bifurcation branches for antiphase oscillation, which was induced by the competition between global feedback and the diffusion effect.

Pulse-coupled Belousov-Zhabotinsky oscillators with frequency modulation

Inhibitory perturbations to the ferroin-catalyzed Belousov-Zhabotinsky (BZ) chemical oscillator operated in a continuously fed stirred tank reactor cause long term changes to the limit cycle: the lengths of the cycles subsequent to the perturbation are longer than that of the unperturbed cycle, and the unperturbed limit cycle is recovered only after several cycles. The frequency of the BZ reaction strongly depends on the acid concentration of the medium. By adding strong acid or base to the perturbing solutions, the magnitude and the direction of the frequency changes concomitant to excitatory or inhibitory perturbations can be controlled independently of the coupling strength. The dynamics of two BZ oscillators coupled through perturbations carrying a coupling agent (activator or inhibitor) and a frequency modulator (strong acid or base) was explored using a numerical model of the system. Here, we report new complex temporal patterns: higher order, partially synchronized modes that develop when inhibitory coupling is combined with positive frequency modulation (FM), and complex bursting patterns when excitatory coupling is combined with negative FM. The role of time delay between the peak and perturbation (the analog of synaptic delays in networks of neurons) has also been studied. The complex patterns found under inhibitory coupling and positive FM vanish when the delay is significant, whereas a sufficiently long time delay is required for the complex temporal dynamics to occur when coupling is excitatory and FM is negative.

Dynamical regime of resorcinol based Belousov–Zhabotinsky chemical oscillator in the presence or absence of some hydrophobic antioxidants in aqueous–organic mixed media

BZ reaction acts as radical generator in AN/DMF mixed solvent system.

Pulse-coupled BZ oscillators with unequal coupling strengths

A host of asymptotically stable, temporally periodic patterns are found when chemical oscillators are pulse coupled,e.g., the 1 : 2 and 1 : D–N type patterns shown here.

Oregonator generalization as a minimal model of quorum sensing in Belousov–Zhabotinsky reaction with catalyst confinement in large populations of particles

The Oregonator demonstrates that quorum sensing in populations of Belousov–Zhabotinsky oscillators arises from modification of the stoichiometry by catalyst confinement.

Dynamics of electrochemical oscillators with electrode size disparity: asymmetrical coupling and anomalous phase synchronization

Experiments are carried out in dual electrode oscillatory Ni electrodissolution in which the two electrodes have different surface areas. The transition to phase synchronization is analyzed as asymmetrical coupling strength, induced by placing a cross resistance between the electrodes, is varied. It is shown that because of nonisochronicity (phase shear, i.e., strong dependence of period on amplitude) of the oscillators, anomalous phase synchronization effects can be observed: advanced/delayed synchronization and, to a lesser extent, frequency difference enhancement. The type of synchronization is strongly affected by the underlying heterogeneities of the oscillators; in the experiments with a slow driver (large surface area) electrode the synchronization is advanced, with a fast driver electrode the synchronization is delayed with respect to symmetrical coupling. The findings thus reveal that the interplay of asymmetrical coupling with the types of inherent heterogeneities plays an important role for the interpretation of size effects in the dynamical behavior of a nonlinear chemical reaction.

Oscillation and synchronization in the combustion of candles

We investigate a simple experimental system using candles; stable combustion is seen when a single candle burns, while oscillatory combustion is seen when three candles burn together. If we consider a set of three candles as a component oscillator, two oscillators, that is, two sets of three candles, can couple with each other, resulting in both in-phase and antiphase synchronization depending on the distance between the two sets. The mathematical model indicates that the oscillatory combustion in a set of three candles is induced by a lack of oxygen around the burning point. Furthermore, we suggest that thermal radiation may be an essential factor of the synchronization.

Synchronization and clustering in a multimode quantum dot laser

We analyze experimentally the intensity oscillations of the longitudinal modes of quantum dot semiconductor lasers. We show that the modal intensities can oscillate chaotically with different average frequencies, but obey a highly organized antiphase dynamics leading to a constant total output power. The fluctuations are in the MHz range. We report the first experimental observation of frequency clustering associated with synchronization. We also observe the propagation of perturbations across the optical spectrum from blue to red.

Entrainment in a Chemical Oscillator Chain with a Pacemaker

Entrainment by a pacemaker was investigated experimentally and numerically in a chain of chemical oscillators using coupled discrete Belousov-Zhabotinsky reaction oscillators. The spontaneous frequency of each oscillator depended on the concentration of catalyst ions. The coupling strengths among the nearest neighbor oscillators were controlled by changing the spacing distance (d) between beads. When the coupling strength was sufficiently strong, the pacemaker entrained other oscillators in the chain. Subsequently, the trigger waves propagating from a pacemaker were observed. The range of trigger wave propagation area, i.e., the number of entrained oscillators, depended on d. Numerical simulation for the system described the experimental results well. Furthermore, photic noise maximized the strength of entrainment at an optimal noise intensity.

Dynamics of a semiconductor laser array with delayed global coupling

We study the dynamics of an array of single mode semiconductor lasers globally but weakly coupled by a common external feedback mirror and by nearest neighbor interactions. We seek to determine the conditions under which all lasers of the array are in phase, whether in a steady, periodic, quasiperiodic, or chaotic regime, in order to maximize the output far field intensity. We show that the delay may be a useful control parameter to achieve in-phase synchronization. For the in-phase steady state, there is a competition between a delay-induced Hopf bifurcation leading to an in-phase periodic regime and a delay-independent Hopf bifurcation leading to an antiphased periodic regime. Both regimes are described analytically and secondary Hopf bifurcations to quasiperiodic solutions are found. Close to the stable steady state, the array is described by a set of Kuramoto equations for the phases of the fields. Above the first Hopf bifurcation, these equations are generalized by the addition of second and third order time derivatives of the phases.

Multidimensional quasiperiodic antiphase dynamics

We study analytically the (N-1)-fold degenerate Hopf bifurcation at which N stationary modes with identical parameters become unstable in a model of a solid-state laser with intracavity second harmonic generation. We use the normal form method and exploit the symmetries of the problem. Up to N=3, stable periodic antiphased solutions emerge from the Hopf bifurcation. For N=4, stable quasiperiodic solutions arise from the degenerate Hopf bifurcation. For N>4, the quasiperiodic solutions may be unstable. Then chaotic itineracy is observed numerically close to the degenerate Hopf bifurcation.