Belousov-Zhabotinsky reaction chemical oscillator

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. 

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]. 

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. 

Some autocatalytic chemical reactions such as the Brusselator and the Belousov-Zhabotinsky reaction schemes can produce temporal oscillations in a stirred homogeneous solution. In the presence of even a small initial concentration inhomogeneity, autocatalytic processes can couple with diffusion to produce organized systems in time and space. 

The Belousov-Zhabotinsky reaction system is one example leading to such chemical oscillations. One of the interesting phenomena is the effect of the very narrow range of controlling parameter /x on the stability of the Belousov-Zhabotinsky reaction system. The following reactions represent the Belousov-Zhabotinsky reaction scheme ... 

One of the best known and studied oscillating reactions is the Belousov-Zhabotinsky reaction. This is the oxidation of an organic compound, like malonic acid, in a sulfuric acid solution by the bromate ion BrOJ. The reaction is catalysed by a redox catalyst like Ce(III)/Ce(IV), Mn(II)/Mn(III) or Fe(phen)3 "/Fe(phen)3". The simplified overall chemical reaction is... 

The Belousov-Zhabotinsky reaction provides an interesting possibility to observe spatial oscillations and chemical wave propagation. If a little less acid and a little more bromide are used in the preparation of the reaction mixture, it is then a stable solution with a red color. After introducing a small fluctuation in the system, blue rings propagate, or even more complex behavior is observed. 

Basin of attraction, see Attraction basin Bell-shaped dependence, of Ca release on Ca, 358,359,379,499 Belousov-Zhabotinsky reaction chaos, 12,283,511 chemical waves, 169,513 excitability, 102,213 oscillations, 1,508 temporal and spatiotemporal organization, 7,169 Bifurcation... 

One of the structural equivalence classes, shown in Fig. 4, has been of particular interest in the study of oscillations in chemical networks with three interacting chemicals. It has appeared " in an analysis of the Field-Noyes equations for the Belousov-Zhabotinsky reaction, and in an analysis of... 

Chemical systems with complex kinetics exhibit a fascinating range of dynamical phenomena. These include periodic and aperiodic (chaotic) temporal oscillation as well as spatial patterns and waves. Many of these phenomena mimic similar behavior in living systems. With the addition of global feedback in an unstirred medium, the prototype chemical oscillator, the Belousov-Zhabotinsky reaction, gives rise to clusters, i.e., spatial domains that oscillate in phase, but out of phase with other domains in the system. Clusters are also thought to arise in systems of coupled neurons. 

Besides these two regimes, another regime, with a temporally periodic change of the chemical composition (chemical oscillation or self-oscillation), may also be observed. A famous example of this phenomenon is the Belousov-Zhabotinsky reaction. Another example of complex kinetic behavior in open chemical systems is the occurrence of multiple steady states due to the fact that for some components of the reaction mixture the rate of consumption and rate of production can be balanced at more than one point. This type of behavior has become the subject of detailed theoretical and computational analyses (Marin and Yablonsky, 2011 Yablonskii et al., 1991). Bespite the fact that there are many experimental data concerning such complex behavior, the steady-state regime with characteristics that are constant in time still is the most observed phenomenon. 

One important feature of reaction-diffusion fields, not shared by fluid dynamical systems as another representative class of nonlinear fields, is worth mentioning. This is the fact that the total system can be viewed as an assembly of a large number of identical local systems which are coupled (i.e., diffusion-coupled) to each other. Here the local systems are defined as those obeying the diffusionless part of the equations. Take for instance a chemical solution of some oscillating reaction, the best known of which would be the Belousov-Zhabotinsky reaction (Tyson, 1976). Let a small element of the solution be isolated in some way from the bulk medium. Then, it is clear that in this small part a limit cycle oscillation persists. Thus, the total system may be imagined as forming a diffusion-coupled field of similar limit cycle oscillators. 

There may be an additional value in studying spatio-temporal chemical turbulence, in connection with its possible relevance to some biological problems. This is expected from the fact that the fields of coupled limit cycle oscillators (or nonoscillating elements with latent oscillatory nature) are often met in living systems. In some cases, such systems show orderly wavelike activities much the same as those observed in the Belousov-Zhabotinsky reaction. There seems to be no reason why we should not expect such organized motion to become unstable and hence show turbulent behavior. The recent work by Ermentrout (1982) who derived a Ginzburg-Landau type equation for neural field seems to be of particular interest in this connection. 

And when the chemicals are placed in a gel everyday Life in a flat dish, the colors appear as a pattern of waves in space rather than as oscillations in time. Chemists have since shown that the Belousov-Zhabotinsky reaction occurs by two different mechanisms, first by one, then by the otho-. These mechanisms are repeated in space or time, depending on the concentrations of intermediate substances. During the reaction, an indicator changes color depending on which mechanism is active. Although the complete set of elementary steps of the Belousov-Zhabotinsky reaction is complicated, the overall reaction occurs just as you would expect. The initial reactants continue to decrease ovct time and the final products increase as the substances come to equilibrium. 

FIGURE 20.22 The oscillating nature of the Belousov-Zhabotinsky reaction can be illustrated by the varying concentrations of some of the species involved. Many of these concentrations are measured electrochemically. Source Reprinted with permission from the Journal of the American Chemical Society, Vol. 94, No. 25, p. 8651. 

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