Instabilities and Patterns in Reaction-Diffusion Systems

Abstract

In a chemical system maintained in non-equilibrium conditions (e.g., by appropriate feeding or when some species remain in excess), various types of instabilities may occur. For example, in a continuously stirred tank reactor, or CSTR (see Fig. 14), one may obtain bistability, temporal oscillations, and chaos. In this type of reactor a permanent feeding is maintained via the inflow and outflow of some reactive species. The concentration and the flow of these species may thus be controlled and used as control parameters. These systems are considered as uniform as the result of the mixing of the chemicals, which is realized by appropriate mechanical means, although some properties of the system may sometimes depend on the stirring. Of course, only temporal patterns may observed in this type of reactor, where chaotic behaviors were first reported in 1977 and induced a large amount of more and more quantitative work, leading, as early as 1979, to the construction of the strange attractor of the Belousov-Zhabotinsky reaction, and the determination of its dimension and its Lyapounov exponents.