Spiral instabilities in media supporting complex oscillations under periodic forcing

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.

Parametric instability-induced synchronization in chemical oscillations and spatiotemporal patterns

We consider a model reaction-diffusion system with two coupled layers in which one of the components in a layer is parametrically driven by a periodic force. On perturbation of a homogeneous stable steady state, the system exhibits parametric instability inducing synchronization in temporal oscillation at half the forcing frequency in absence of diffusion and spatiotemporal patterns in presence of diffusion, when strength of parametric forcing and the strength of coupling are kept above their critical thresholds. We have formulated a general scheme to derive analytically the critical thresholds and dispersion relation to locate the unstable spatial modes lying between the tilted Arnold tongue in the amplitude-frequency plot. Full numerical simulations on Gierer-Meinhardt activator-inhibitor model corroborate our theoretical analysis on parametric instability-induced antiphase synchronization in chemical oscillation and spatiotemporal pattern formation, between the two layers.

Parametric spatiotemporal oscillation in reaction-diffusion systems

We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.