Periodic perturbation of one of two identical chemical oscillators coupled via inhibition

Drastic effects of an inert Pt wire on the redox behavior of the Belousov-Zhabotinsky reaction

This research investigated responses of the Belousov-Zhabotinsky (BZ) reaction to the presence of a chemically inert Pt wire in solution. Experiments showed that connecting the Pt wire to a neutral ground caused a spontaneous drastic shift in the redox potential and might even induce complex behavior. Characterizations using an unstirred ferriin solution demonstrated the formation of a red colored propagating front at the grounded Pt wire, suggesting the reduction of ferriin to ferroin. Measurements with different combinations of electrodes in both stirred and reaction-diffusion media further confirmed the reduction of BZ metal catalysts at the Pt wire and the accompanying oxidation reaction at the reference electrode. The observed drastic change in redox potential and oscillation waveform can be understood based on the passive reduction reaction at the indicator electrode that is connected to the reference electrode through a potential meter. The obtained influence can be further manipulated by adding a resistor between the Pt wire and the neutral ground, making this convenient perturbation method attractive for the study of redox chemical reaction dynamics.

Size- and position-dependent bifurcations of chemical microoscillators in confined geometries

The present theoretical study deals with microparticles (beads) that contain an immobilized Belousov-Zhabotinsky (BZ) reaction catalyst. In the theoretical experiment, a BZ bead is immersed in a small water droplet that contains all of the BZ reaction reagents but no catalyst. Such heterogeneous reaction-diffusion BZ systems with the same BZ reactant concentrations demonstrate various dynamic modes, including steady state and low-amplitude, high-amplitude, and mixed-mode oscillations (MMOs). The emergence of such dynamics depends on the sizes of the bead and water droplet, as well as on the location of the bead inside the droplet. MMO emergence is explained by time-delayed positive feedback in combination with a canard phenomenon. If two identical BZ beads are immersed in the same droplet, many different dynamic modes including chaos are observed.

Unraveling the diverse nature of electric field induced spatial pattern formation in Gray-Scott model

We have considered a Gray-Scott kind of model chemical reaction-diffusion system that comprises ionic reactants and auto-catalysts to investigate the possibilities of mobility induced spatial pattern formation under the influence of an external electric field. Our study reveals that applying a uni-directional electric field can deform the already existing Turing patterns obtained due to diffusion driven instability, but cannot produce mobility driven instability and consequent spatial patterns in the absence of diffusion driven instability for a Gray-Scott like system. However, application of the electric field along two mutually perpendicular directions produces a mobility induced pattern in the absence of any differences in the diffusivities of the corresponding chemical reactants. Additionally, we have shown a systematic way to predict the range of absolute values of the pair of electric field intensities along two directions that will lead to spatially heterogeneous patterns in the absence of diffusion driven instability. Our study further demonstrates that the stability of the patterns formed and the nature of the patterns evolved varies with the increasing level of electric field intensities. The insights gained from this study will allow us to develop future experimental strategies to produce diverse range of stable and unique spatial patterns.

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.

Excitatory and inhibitory coupling in a one-dimensional array of Belousov-Zhabotinsky micro-oscillators: theory

We study numerically the behavior of one-dimensional arrays of aqueous droplets containing the oscillatory Belousov-Zhabotinsky reaction. Droplets are separated by an oil phase that allows coupling between neighboring droplets via two species: an inhibitor, Br(2), and an activator, HBrO(2). Excitatory coupling alone (through the activator) generates in-phase oscillations and/or "waves," while inhibitory coupling alone (through Br(2)) gives rise to antiphase oscillations, Turing patterns, and their combinations. The simultaneous presence of excitatory and inhibitory coupling leads to a large number of new spatiotemporal patterns, including some that exhibit very complex behavior. Analysis of a simple model allows us to simulate patterns resembling those observed experimentally under similar conditions and to elucidate the contributions of droplet and gap sizes, activator and inhibitor partition coefficients, and malonic acid concentration to the coupling strengths.

Phase and frequency entrainment in locally coupled phase oscillators with repulsive interactions

Recent experiments in one- and two-dimensional microfluidic arrays of droplets containing Belousov-Zhabotinsky reactants show a rich variety of spatial patterns [M. Toiya et al., J. Phys. Chem. Lett. 1, 1241 (2010)]. The dominant coupling between these droplets is inhibitory. Motivated by this experimental system, we study repulsively coupled Kuramoto oscillators with nearest-neighbor interactions, on a linear chain as well as a ring in one dimension, and on a triangular lattice in two dimensions. In one dimension, we show using linear stability analysis as well as numerical study that the stable phase patterns depend on the geometry of the lattice. We show that a transition to the ordered state does not exist in the thermodynamic limit. In two dimensions, we show that the geometry of the lattice constrains the phase difference between two neighboring oscillators to 2π/3. We report the existence of domains with either clockwise or anticlockwise helicity, leading to defects in the lattice. We study the time dependence of these domains and show that at large coupling strengths the domains freeze due to frequency synchronization. Signatures of the above phenomena can be seen in the spatial correlation functions.