Chemical oscillations and biological rhythms
Rhythms are among the most conspicuous properties of living systems. They occur at all levels of biological organization, from unicellular to multicellular organisms, with periods ranging from fractions of a second to years (Table 1.1). In humans, the cardiac and respiratory functions and the circadian rhythm of sleep and wakefulness point to the key role of periodic processes in the maintenance of life. In spite of their close association with physiology, however, periodic phenomena are by no means restricted to living systems. Since the discovery of the oscillatory chemical reaction of Belousov and Zhabotinsky (Belousov, 1959; Zhabotinsky, 1964; Tyson, 1976), it has become clear over the last three decades (Nicolis & Portnow, 1973; Noyes & Field, 1974; Pacault et al, 1976; Epstein, 1983, 1984; Field & Burger, 1985) that numerous chemical reactions studied in the laboratory display periodic behaviour in the course of time. Biological rhythms nevertheless remain more common than oscillations in purely chemical systems.
However, oscillatory behaviour does not always possess a simple periodic nature. Thus, both in chemistry and biology, oscillations sometimes present complex patterns of bursting, in which successive trains of high-frequency spikes are separated at regular intervals by phases of quiescence. Yet another mode of complex oscillatory behaviour, which has received increased attention over the last decade, is characterized by its aperiodic nature and sensitivity to initial conditions. Such chaotic oscillations have been observed in chemical reactions (Scott, 1991; Field & Gyorgi, 1993) and in a variety of biological contexts (Olsen & Degn, 1985; Holden, 1986; Glass & Mackey, 1988).