Chaotic Behavior in Simple Reaction Systems

Abstract

Deterministic nonperiodic flow (of “chaotic” or “strange” or “tumbling” type, respectively) was first observed, in a 3-component differential system, by E. N. Lorenz in 1963. A 3-component abstract reaction system showing the same qualitative behavior is indicated. It consists of (1) an ordinary 2-variable chemical oscillator and (2) an ordinary single-variable chemical hysteresis system. According to the same dual principle, many more analogous systems can be devised, no matter whether chemical, biochemical, biophysical, ecological, sociological, economic, or electronic in nature. Their dynamics are determined by the presence of a “folded” Poincaré map. Under numerical simulation, the proposed chemical system provides an almost ideal illustration to the underlying dynamical prototype, the “3-dimensional blender”. Thus, continuous Euklidean dynamics (and with it chemical kinetics) proves to be of equal interest in studying chaos as discrete dynamical systems already have.