Belousov-Zhabotinskii reaction discussion

As we have already commented, mappings of the type discussed above are not in any way easily related to a given set of reaction rate equations. Such mappings have, however, been used for chemical systems in a slightly different way. A quadratic map has been used to help interpret the oscillatory behaviour observed in the Belousov-Zhabotinskii reaction in a CSTR. There, the variable x is not a concentration but the amplitude of a given oscillation. Thus the map correlates the amplitude of one peak in terms of the amplitude of the previous excursion. 

At the end of this chapter we will now briefly discuss a theoretical approach to the description of chaotic processes encountered in chemical kinetics, see Section 1.3 and Sections 6.2.2.4, 6.3.2.4. In Section 6.2.2.4 we described the method of generation and physical meaning of a chaotic state of the Belousov-Zhabotinskii reaction carried out in a flow reactor. 

I present in this chapter a short discussion of chemical reaction rate laws and mechanisms, and of nonlinear ordinary and partial differential equations. To strengthen the connection between this review material and the later chapters, I have drawn the examples and problems here from literature relevant to the Belousov-Zhabotinskii reaction. 

It may be for one of these reasons that you have read thus far. In these lecture notes, which list heavily to the mathematical side, I have tried to present a consistent, self-contained discussion of temporal and spatial organization in the Belousov-Zhabotinskii reaction. They are not... 

Since the discovery of the Belousov-Zhabotinskii (B-Z) reaction a large number of variations of this reaction has been investigated by numerous researchers. Both experimental and theoretical investigations outnumber those for any other oscillatory reaction. The reason for this extensive interest comes from the fact that the B-Z reaction is very rich in its interesting dynamical behavior and its variations are quite extensive. In this section research done during the period of 1980-82 is discussed briefly. 

Several theoretical studies have attempted to relate the period of an oscillating chemical reaction to parameters such as the rate constants in the kinetic model. Aspects of theoretical models for the Belousov-Zhabotinskii (B-Z) reaction have been discussed. ... 

The Wolf and Swift method has been tested on model systems with known Lyapunov spectra and applied to data for the Belousov-Zhabotinskii chemical reaction and Couette-Taylor flow. See refs. [36-37] for a discussion of the requirements on accuracy and the size of a data file. 

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