Spiral pattern in chlorite-iodide-malonic acid reaction: A theoretical and numerical study

Radially evolving spiral wave patterns in the Gierer-Meinhardt reaction-diffusion system

Spiral wave formation in spatially extended systems is a fascinating phenomenon that has garnered significant attention in reaction-diffusion systems. In this study, we explore the emergence of spiral wave-like patterns in the Gierer-Meinhardt reaction-diffusion model. By employing a multiple-time scale perturbation technique, we derive amplitude equations that reveal the conditions for spiral wave formation. Notably, our analysis shows that the amplitude of these spiral waves varies with the radial distance, introducing a distinctive feature to this pattern. Our theoretical predictions are further substantiated by numerical simulations, which confirm the emergence of spiral wave structures and validate the distinct radial dependence of their amplitude.

Amplitude-mediated spiral chimera pattern in a nonlinear reaction-diffusion system

Formation of diverse patterns in spatially extended reaction-diffusion systems is an important aspect of study that is pertinent to many chemical and biological processes. Of special interest is the peculiar phenomenon of chimera state having spatial coexistence of coherent and incoherent dynamics in a system of identically interacting individuals. In the present article, we report the emergence of various collective dynamical patterns while considering a system of prey-predator dynamics in the presence of a two-dimensional diffusive environment. Particularly, we explore the observance of four distinct categories of spatial arrangements among the species, namely, spiral wave, spiral chimera, completely synchronized oscillations, and oscillation death states in a broad region of the diffusion-driven parameter space. Emergence of amplitude-mediated spiral chimera states displaying drifted amplitudes and phases in the incoherent subpopulation is detected for parameter values beyond both Turing and Hopf bifurcations. Transition scenarios among all these distinguishable patterns are numerically demonstrated for a wide range of the diffusion coefficients which reveal that the chimera states arise during the transition from oscillatory to steady-state dynamics. Furthermore, we characterize the occurrence of each of the recognizable patterns by estimating the strength of incoherent subpopulations in the two-dimensional space.

Differential-flow-induced transition of traveling wave patterns and wave splitting

We have analyzed the differential flow-induced instability in the presence of diffusive transport in a reaction-diffusion system following activator-inhibitor kinetics. The conspicuous interaction of differential flow and differential diffusivity that leads to pattern selection during transition of the traveling waves from stripes to rotating spots propagating in hexagonal arrays subsequent to wave splitting has been explored on the basis of a few-mode Galerkin scheme.

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.

Sodium chlorite – iodide – acetylacetone oscillation reaction investigated by UV-Vis spectrophotometry

A new sodium chlorite – iodide – acetylacetone chemical oscillatory reaction has been studied by the UV-Vis spectrophotometric method. The initial concentrations of acetylacetone, sodium chlorite, iodide, and sulfuric acid and the pH value have great influence on the oscillation observed at a wavelength of 570 nm for the starch–triiodide complex. There is a pre-oscillatory or induction stage and the amplitude and number of oscillations depend on the initial concentration of the reactants. Equations for the starch–triiodide complex reaction rate change with reaction time and the initial concentrations in the oscillation stage were obtained. The induction time decreases linearly with the initial concentration of acetylacetone or sodium chlorite but increases linearly with the initial concentration of sulfuric acid. The oscillation reaction can be accelerated by increasing the reaction temperature. The apparent activation energies at the induction stage and the oscillation stage were 61.02 and 61.36 kJ/mol, respectively, indicating that the two stages have similar reaction mechanisms. Generating the enol isomer by keto–enol tautomerism is an important step to constrain the time of the induction period.

Chemical oscillator as a generalized Rayleigh oscillator

We derive the conditions under which a set of arbitrary two dimensional autonomous kinetic equations can be reduced to the form of a generalized Rayleigh oscillator which admits of limit cycle solution. This is based on a linear transformation of field variables which can be found by inspection of the kinetic equations. We illustrate the scheme with the help of several chemical and bio-chemical oscillator models to show how they can be cast as a generalized Rayleigh oscillator.

Chlorine dioxide-iodide-methyl acetoacetate oscillation reaction investigated by UV-vis and online FTIR spectrophotometric method

In order to study the chemical oscillatory behavior and mechanism of a new chlorine dioxide-iodide ion-methyl acetoacetate reaction system, a series of experiments were done by using UV-Vis and online FTIR spectrophotometric method. The initial concentrations of methyl acetoacetate, chlorine dioxide, potassium iodide, and sulfuric acid and the pH value have great influence on the oscillation observed at wavelength of 289 nm. There is a preoscillatory or induction period, and the amplitude and the number of oscillations are associated with the initial concentration of reactants. The equations for the triiodide ion reaction rate changing with reaction time and the initial concentrations in the oscillation stage were obtained. Oscillation reaction can be accelerated by increasing temperature. The apparent activation energies in terms of the induction period and the oscillation period were 26.02 KJ/mol and 17.65 KJ/mol, respectively. The intermediates were detected by the online FTIR analysis. Based upon the experimental data in this work and in the literature, a plausible reaction mechanism was proposed for the oscillation reaction.

Experimental Study of Closed System in the Chlorine Dioxide-Iodide-Sulfuric Acid Reaction by UV-Vis Spectrophotometric Method

The mole ratio r(r = [I⁻]₀/[ClO₂]₀) has great influence on ClO₂-I⁻-H₂SO₄ closed reaction system. By changing the initiate concentration of potassium iodide, the curve of absorbance along with the reaction time was obtained at 350 nm and 297 nm for triiodide ion, and 460 nm for iodine. The changing point of the absorbance curve's shape locates at r = 6.00. For the reaction of ClO₂-I⁻ in the absence of H₂SO₄, the curve of absorbance along with the reaction time can be obtained at 350 nm for triiodide ion, 460 nm for iodine. The mole ratio r is equal to 1.00 is the changing point of the curve's shape no matter at which wavelength to determine the reaction. For the reaction of ClO₂-I⁻-H⁺ in different pH buffer solution, the curve of absorbance along with the reaction time was recorded at 460 nm for iodine. When r is greater than 1.00, the transition point of the curve's shape locates at pH 2.0, which is also the point of producing chlorite or chloride for chlorine dioxide at different pH. When r is less than 1.00, the transition point locates at pH 7.0.