Zaikin-Zhabotinsky reaction

In an interesting variant of the CA model, cells can adopt "excited states." This has been used to model the spatial waves observed in the Zaikin-Zhabotinsky reaction. 

Reaction-diffusion systems can readily be modeled in thin layers using CA. Since the transition rules are simple, increases in computational power allow one to add another dimension and run simulations at a speed that should permit the simulation of meaningful behavior in three dimensions. The Zaikin-Zhabotinsky reaction is normally followed in the laboratory by studying thin films. It is difficult to determine experimentally the processes occurring in all regions of a three-dimensional segment of excitable media, but three-dimensional simulations will offer an interesting window into the behavior of such systems in the bulk. 

Expanding target patterns in the Belousov-Zhabotinsky reaction were first discovered by Zaikin and Zhabotinsky (1970). In their experiment, they used a spontaneously oscillating thin layer of solution which was contained in a Petri dish of diameter 100 mm. The reagent contained bromate, bromomalonic acid and ferroin. With this prescription, one may observe periodic alternation of oxidized and reduced forms of the catalyst through a dramatic color change of the solution between red (reduced state) and blue (oxidized state). Some features of the pattern observed by them and by later experimenters are the following . ... 

A classical example of an inorganic set of coupled reactions, some of them being autocatalytic, occurs in the Belousov-Zhabotinsky reaction. This reaction, discovered in 1958 by B.P. Belousov and reported to the western world by A.N. Zaikin and A.M. Zhabotinsky in 1970, is the most investigated and best understood... 

A. M. Zhabotinsky, Periodic Kinetics of Oxidation of Malonic Acid in Solution (Study of the Belousov Reaction Kinetics). Biofizika 1964, 9, 306-311 A. N. Zaikin, A. M. Zhabotinsky, Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System. Nature 1970, 225, 535-537. See, also, a conversation with Anatol M. Zhabotinsky, I. Hargittai, Candid Science III More Conversions with Famous Chemists. (ed. M. Hargittai.) Imperial College Press, London, 2003, pp. 432-447. 

In 1980, the Lenin prize was awarded to Belousov, Zhabotinsky, V. I. Krinsky, G. R. Ivanitsky, and A. Zaikin for their work on the BZ reaction. Belousov had died in 1970. 

Probably the first examples of complex periodic oscillations in chemistry are found in studies of the BZ reaction in a CSTR in the mid-1970s. In these experiments, a number of investigators (Zaikin and Zhabotinsky, 1973 Sorensen, 1974 Marek and Svobodova, 1975 De Kepper et al., 1976 Graziani et al., 1976) observed bursting, a form of oscillation commonly seen in neurons, but previously unobserved in simple chemical reactions. Bursting consists of periods of relatively... 

Zaikin, A. N. Zhabotinsky, A. M. 1973. A Study of a Self-Oscillatory Chemical Reaction II. Influence of Periodic External Force, in Biological and Biochemical Oscillators (Chance, B. Pye, E. K. Ghosh, A. K. Hess, B., Eds.). Academic Press New York pp. 81-88. 

Hudson, J. L., Hart, M., Marinko, D. (1979) An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov-Zhabotinskii reaction. J. Chem. Phys. 71, 1601 Ivanitsky, G. R., Krinsky, V. I., Zaikin, A. N., Zhabotinsky, A. M. (1981) Autowave processes and their role in disturbing the stability of distributed excitable systems. In Soviet Scientific Reviews, Section D, Biological Reviews 2, ed. by V. P. Skulachev (Soviet Scientific Reviews) p. 279 Joseph, D. D., Sattinger, D. H. (1972) Bifurcating time periodic solutions and their stability. Arch. Rational. Mech. Anal. 45, 79... 

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