Chemical Oscillators

Nonlinear chemical reactions can spontaneously oscillate (Hopf bifurcation) or produce chaos. Explore four classic models: Brusselator, Oregonator (BZ reaction), Lorenz, and the Repressilator genetic oscillator.

Model Parameter A 1.0 Parameter B 3.0

Brusselator
ẋ = A − (B+1)x + x²y
ẏ = Bx − x²y
Hopf bifurcation at B = A²+1

The Belousov-Zhabotinsky reaction (1951/1964) was the first observed chemical oscillator — initially dismissed as impossible by reviewers. The Brusselator (Prigogine, 1967) and Oregonator (Field-Körös-Noyes, 1972) are its mathematical models. The repressilator (Elowitz-Leibler, 2000) implemented this in E. coli using three genes in a ring of mutual repression — a synthetic biology landmark.