There is no doubt that the phenomenon of chemical oscillation—the periodic or nearly periodic temporal variation of concentrations in a reacting system— provided the initial impetus for the development of nonlinear chemical dynamics, and has continued to be the most thoroughly studied of the phenomena that constitute this rich field. In our opening chapter, we alluded to the early skepticism that experimental observations of chemical oscillation engendered. We also noted that the first chemical oscillators were discovered accidentally, by researchers looking for other phenomena. It is relatively easy to understand intuitively why a typical physical oscillator, like a spring, should behave in a periodic fashion. It is considerably more difficult for most of us to see how a chemical reaction might undergo oscillation. As a result, the thought of building a physical oscillator seems far more reasonable than the notion of designing an oscillatory chemical reaction. In this chapter, we will examine how chemical oscillation can arise, in general, and how it is possible to create chemical reactions that are likely to show oscillatory behavior. In the next chapter, we will discuss how to take a chemical oscillator apart and analyze why it oscillates—the question of mechanism. We also look in detail there at the mechanisms of several oscillating reactions. In order to gain some insight into how oscillation might arise in a chemical system, we shall consider a very simple and general model for a reaction involving two concentrations, u and v. Two independent concentration variables is the smallest number that can generate oscillatory behavior in a chemical system. The basic idea, however, is applicable to many-variable systems, because the essential features of the dynamics are often controlled by a small number of variables, and the other variables simply follow the behavior of the key species.
Temperature Control of Continuous Chemical Reactors Under Noisy Measurements and Model Uncertainties
