Nonlinear chemical dynamics Belousov-Zhabotinsky

Despite the importance of the chlorite-iodide systems in the development of nonlinear chemical dynamics in the 1980s, the Belousov-Zhabotinsky(BZ) reaction remains as the most intensively studied nonlinear chemical system, and one displaying a surprising variety of behavior. Oscillations here were discovered by Belousov (1951) but largely unnoticed until the works of Zhabotinsky (1964). Extensive description of the reaction and its behavior can be found in Tyson (1985), Murray (1993), Scott (1991), or Epstein and Pojman (1998). There are several versions of the reaction, but the most common involves the oxidation of malonic acid by bromate ions BrOj in acid medium and catalyzed by cerium, which during the reaction oscillates between the Ce3+ and the Ce4+ state. Another possibility is to use as catalyst iron (Fe2+ and Fe3+). The essentials of the mechanisms were elucidated by Field et al. (1972), and lead to the three-species model known as the Oregonator (Field and Noyes, 1974). In this... 

The study of nonlinear chemical dynamics begins with chemical oscillators - systems in which the concentrations of one or more species increase and decrease periodically, or nearly periodically. While descriptions of chemical oscillators can be found at least as far back as the nineteenth century (and chemical oscillation is, of course, ubiquitous in living systems), systematic study of chemical periodicity begins with two accidentally discovered systems associated with the names of Bray (2) and of Belousov and Zhabotinsky (BZ) 3,4), These initial discoveries were met with skepticism by chemists who believed that such behavior would violate the Second Law of Thermodynamics, but the development of a general theory of nonequilibrium thermodynamics (5) and of a detailed mechanism 6) for the BZ reaction brought credibility to the field by the mid-1970 s. Oscillations in the prototypical BZ reaction are shown in Figure 1. 

Although some of the fimdamental discoveries in nonlinear chemical dynamics were made at the beginning of the twentieth century and arguably even earlier, the field itself did not emerge until the mid-1960 s, when Zhabotinsky s development (1) of the oscillatory reaction discovered by Belousov (2) finally convinced a skeptical chemical community that periodic reactions were indeed compatible with the Second Law of Thermodynamics as well as all other known rules of chemistry and physics. Since the discovery of the Belousov-Zhabotinsky (BZ) reaction, nonlinear chemical dynamics has grown rapidly in both breadth and depth (3). 

We have seen that the Belousov-Zhabotinsky reaction, even in the restricted parameter range for which some elementary analysis can be done, has a large variety of behaviors, which makes it the ideal model system to illustrate nonlinear dynamics of chemical systems. We briefly mention here a kinetic system of a rather different origin, the FitzHugh-Nagumo (FN) model (Murray, 1993 Meron, 1992) ... 

One important feature of reaction-diffusion fields, not shared by fluid dynamical systems as another representative class of nonlinear fields, is worth mentioning. This is the fact that the total system can be viewed as an assembly of a large number of identical local systems which are coupled (i.e., diffusion-coupled) to each other. Here the local systems are defined as those obeying the diffusionless part of the equations. Take for instance a chemical solution of some oscillating reaction, the best known of which would be the Belousov-Zhabotinsky reaction (Tyson, 1976). Let a small element of the solution be isolated in some way from the bulk medium. Then, it is clear that in this small part a limit cycle oscillation persists. Thus, the total system may be imagined as forming a diffusion-coupled field of similar limit cycle oscillators. 

---