My Nguyen
Dr. Reden
Calculus Honors
May 19th, 2016
Dynamical system project: Brusselator
Chemical Oscillators have only been recognized as mainstream science since the
1960s. There was a prior belief that all chemical reactions progressed in one direction
(monotonically) to equilibrium. First oscillating reaction discovered around 1950 by Boris
Pavlovich Belousov. Solution of citric acid in water with acidified bromate and ceric ions
oscillated from colorless to yellow for up to an hour. However, Belousov’s work ill-received
by scientific community. Anatol Zhabotinsky then continued his work in 1961. Zhabotinsky
succeeded in awakening the scientific community to the validity of chemical oscillators. The
cerium-bromate reaction became known as the Belousov-Zhabotinsky (BZ) Reaction. Today,
many chemical systems are known to oscillate and various mathematical models have been
developed to describe the BZ reaction such as a Brusselator model and Oregonator model. To
date, however, the actual reaction mechanism remains a mystery. The reaction mechanism to
be studied, commonly called the Brusselator, is an example of an autocatalytic, oscillating
chemical reaction. An autocatalytic reaction is one in which a species acts to increase the rate
of its producing reaction.
The vast majority of chemical reactions proceed to equilibrium through a monotonic
mechanism. In recent years, however, nonlinear, oscillating chemical reactions have been
widely studied, characterized, and modeled. Such chemical reactions share remarkable
similarities with biological and neuronal processing that are capable of timing, switching, and
signal propagation (Strizhak and Menzinger, 1996). Related reactions such as the Brusselator
and the Belousov-Zhabotinsky reaction both display similar behavior and can be modeled
