Belousov-Zhabotinsky reaction system

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

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 ... 

Another type of dynamic self-organization, so-called dissipative structure , is known as a general physical phenomenon which is generated under chemical or physical conditions far from equilibrium [238]. Many spatiotemporal patterns of the dissipative structures are formed in the dissipative processes ranging in size from sub-micrometers to hundreds of kilometers. Several types of regular patterns, e.g. spirals in the Belousov-Zhabotinsky reaction systems, the honeycomb and stripes of Rayleigh/Benard convection, are formed as spatiotemporal patterns in the dissipative processes. To utilize the dissipative structures for self-organization of molecular assemblies, the spatiotemporal patterns have to be frozen as stationary stable structures. 

Yang LF, Dolnik M, Zhabotinsky AM, Epstein IR (2000) Oscillatory clusters in a model of the photosensitive Belousov-Zhabotinsky reaction system with globed feedback. Phys Rev E 62 6414-6420... 

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. 

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. 

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. 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 (

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 following model [57] appearing in case 3.13-5, which simulates the Belousov-Zhabotinski reaction, was applied also for the open system ... 

P.De Kepper and K.Bar-Eli, Dynamical Properties of the Belousov-Zhabotinski Reaction in a Flow System. Theoretical and Experimental Analysis, The Journal of Physical Chemistry, 87,480-488(1983). 

Experimentally dissipative structures in chemical systems have been observed. The best known are probably the Belousov-Zhabotinski reactions. Already two articles describing them have appeared in Scientific American, in the issues of June 1974 and July 1978. 

Oscillatory reactions provide one of the most active areas of research in contemporary chemical kinetics and two published studies on the photochemistry of Belousov-Zhabotinsky reaction are very significant in this respect. One deals with Ru(bpy)3 photocatalysed formation of spatial patterns and the other is an analysis of a modified complete Oregonator (model scheme) system which accounts for the O2 sensitivity and photosensitivity. ... 

We have seen that the Belousov-Zhabotinsky reaction, even in the restricted parameter range for which some elementary analysis can be done, has a large variety of behaviors, which makes it the ideal model system to illustrate nonlinear dynamics of chemical systems. We briefly mention here a kinetic system of a rather different origin, the FitzHugh-Nagumo (FN) model (Murray, 1993 Meron, 1992) ... 

The experimental system employed in this paper is the light-sensitive Belousov-Zhabotinsky reaction. For numerical simulations only the underlying Oregonator model was used. However, our theoretical approach is based on a very general description of excitable media and does not rely on specific features of any experimental or model system. Therefore, our results are of general character, and can be applied to control spiral wave... 

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. 

The spiral or concentric waves observed for the spatial distribution of cAMP (fig. 5.6) present a striking analogy with similar wavelike phenomena found in oscillatory chemical systems, of which the Belousov-Zhabotinsky reaction (fig. 5.7) provides the best-known example (Winfree, 1972a). 

Reducing the dynamics of a complex system to that of a two-variable system is the goal pursued in most studies devoted to periodic or excitable behaviour, in chemistry as in biology. The main impetus for such a reduction is that it allows us to study these phenomena by means of phase plane analysis. The latter clarifies the origin of the two modes of dynamic behaviour, and highlights basic features common to different systems. This approach was followed in the study of excitability and oscillations in the Belousov-Zhabotinsky reaction (Tyson, 1977), and in... 

Roux, J.C. 1993. Dynamical systems theory illustrated chaotic behavior in the Belousov-Zhabotinsky reaction. In Chaos in Chemistry and Biochemistry. R.J. Field L. Gyorgyi, eds. World Scientific, Singapore, pp. 21-46. 

Tomita, K. I. Tsuda. 1979. Chaos in the Belousov-Zhabotinsky reaction in a flow system. Phys. Lett. 71A 489-92. 

By now we know a large number of oscillatory reactions, not only in chemistry - as exemplified by the famous Belousov-Zhabotinsky reaction - but also in biochemical and cellular systems. It is interesting to observe that in oscillations in inorganic chemistry the molecules are simple but the mechanisms are highly complex, whereas in biochemistry the molecules responsible for rhythmic phenomena possess a complex structure (enzymes or receptors. ..) whereas the mechanisms often are simple. 

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