Including a chapter on biological oscillators was not an easy decision. In one sense, no book on nonlinear chemical dynamics would be complete without such a chapter. Not only are the most important and most numerous examples of chemical oscillators to be found in living systems, but the lure of gaining some insight into the workings of biological oscillators and into the remarkable parallels between chemical and biological oscillators attracts many, perhaps most, new initiates to the study of “exotic” chemical systems. On the other hand, it is impossible for us to do even a minimal job of covering the ground that ought to be covered, either in breadth or in depth. To say that the subject demands a whole book is to understate the case badly. There are indeed whole books, many of them excellent, devoted to various aspects of biological oscillators. We mention here only four of our favorites, the volumes by Winfree (1980), Glass and Mackey (1988), Murray (1993) and Goldbeter (1996). Having abandoned the unreachable goal of surveying the field, even superficially, we have opted to present brief looks at a handful of oscillatory phenomena in biology. Even here, our treatment will only scratch the surface. We suspect that, for the expert, this chapter will be the least satisfying in the book. Nonetheless, we have included it because it may also prove to be the most inspiring chapter for the novice. The range of periods of biological oscillators is considerable, as shown in Table 13.1. In this chapter, we focus on three examples of biological oscillation: the activity of neurons; polymerization of microtubulcs; and certain pathological conditions, known as dynamical diseases, that arise from changes in natural biological rhythms. With the possible exception of the first topic, these are not among the best-known nor the most thoroughly studied biological oscillators; they have been chosen because we feel that they can be presented, in a few pages, at a level that will give the reader a sense of the fascinating range of problems offered by biological systems.
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