Belousov-Zhabotinski Reaction

Gyorgyi L and Field R J 1992 A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction Nature 355 808-10... 

An example of the application of J2-weighted imaging is afforded by the imaging of the dynamics of chemical waves in the Belousov-Zhabotinsky reaction shown in figure B 1.14.5 [16]. In these images, bright... 

Figure Bl.14.5. J2-weighted images of the propagation of chemical waves in an Mn catalysed Belousov-Zhabotinsky reaction. The images were acquired in 40 s intervals (a) to (1) using a standard spin echo pulse sequence. The slice thickness is 2 nun. The diameter of the imaged pill box is 39 nun. The bright bands...

Fig. 5 MR images of traveling (reaction-diffusion)waves in the manganese-catalysed Belousov-Zhabotinsky reaction, taken from the centre of a bed packed with 1 mm diameter glass spheres (22). Waves are formed both inside the bed and above it in the liquid phase. Images (a-d) are shown at time intervals of 16 s. 

The 1970s saw an explosion of theoretical and experimental studies devoted to oscillating reactions. This domain continues to expand as more and more complex phenomena are observed in the experiments or predicted theoretically. The initial impetus for the smdy of oscillations owes much to the concomitance of several factors. The discovery of temporal and spatiotemporal organization in the Belousov-Zhabotinsky reaction [22], which has remained the most important example of a chemical reaction giving rise to oscillations and waves. 

At the same time as the Belousov-Zhabotinsky reaction provided a chemical prototype for oscillatory behavior, the first experimental studies on the reaction catalyzed by peroxidase [24] and on the glycolytic system in yeast (to be discussed in Section 111) demonstrated the occurrence of biochemical oscillations in vitro. These advances opened the way to the study of the molecular bases of oscillations in biological systems. 

S. Vajda and T. Tur3nyi, Principal component analysis for reducing the Edelsan-Field-Noyes model of Belousov-Zhabotinsky reaction, J. Phys. Chem. 

Despite the fact that from a principal point of view a problem of concentration oscillations could be considered as solved [4], satisfactory theoretical descriptions of experimentally well-studied particular reactions are practically absent. Due to very complicated reaction mechanism (in order to describe the Belousov-Zhabotinsky reaction even in terms of standard chemical kinetics several tens of concentration equations for intermediate products should be written down and solved numerically [4, 9, 10]) these equations contain large number of ill-defined parameters - reaction rates [10]. 

As it follows from the above-said, nowadays any study of the autowave processes in chemical systems could be done on the level of the basic models only. As a rule, they do not reproduce real systems, like the Belousov-Zhabotinsky reaction in an implicit way but their solutions allow to study experimentally observed general kinetic phenomena. A choice of models is defined practically uniquely by the mathematical formalism of standard chemical kinetics (Section 2.1), generally accepted and based on the law of mass action, i.e., reaction rates are proportional just to products of reactant concentrations. 

Hudson, J. L., Hart, M. and Marinko, D., 1979, An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov-Zhabotinski reaction. J. Chem. Phys. 71,1601-1606. 

One of the well-studied systems that illustrates this successive-bifurcation behavior is the Belousov-Zhabotinski reaction. Let me briefly show you the results of some experiments done at the University of Texas at Austin,8 referring for further details to the discussion by J. S. Turner in this volume. The experimental setup of the continuously stirred reactor... 

Fig. 5. Experimental arrangement of the continuously stirred Belousov-Zhabotinski reaction.

Fig. 7. Mixed mode oscillations in the Belousov-Zhabotinski reaction when it is farther from equilibrium than it is in Fig. 6.

Fig. 8. When the Belousov-Zhabotinski reaction is sufficiently far from equilibrium it shows a chaotic behavior. This is reflected in the power spectrum being flat in comparison with the spectrum of the more orderly oscillatory behavior.

Fig. 9. A schematic representation of the different types of nonequilibrium behavior in the Belousov-Zhabotinski reaction.

COMPLEX PERIODIC AND NONPERIODIC BEHAVIOR IN THE BELOUSOV-ZHABOTINSKI REACTION... 

Fig. 3. Experimental traces of bromide ion concentration in closed system studies of the Belousov-Zhabotinski reaction, showing (a) quasiharmonic (i.e., sinusoidal) oscillations, (A>) and (c) increasingly nonlinear oscillations, and (

Diffusional process and chemical reaction synchronization induces oscillations of reaction product yields. This common type of synchronous reactions in the literature is referred to as the Belousov-Zhabotinsky reaction. 

Modeling of the Stirring Effect in the Autocatalytic Step of the Belousov—Zhabotinsky Reaction. 

Tsuda, Ichiro, "On the abnormality of period doubling bifurcation in connection with the bifurcation structure in. the Belousov-Zhabotinsky reaction system", preprint (1981). 

Another aspect of a very different nature also merits attention. For complex reaction schemes, it can be very cumbersome to write the appropriate set of differential equations and their translation into computer code. As an example, consider the task of coding the set of differential equations for the Belousov-Zhabotinsky reaction (see Section 7.5.2.4). It is too easy to make mistakes and, more importantly, those mistakes can be difficult to detect. For any user-friendly software, it is imperative to have an automatic equation parser that compiles the conventionally written kinetic model into the correct computer code of the appropriate language [37-39],... 

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