The Brusselator is a theoretical model for a type of
autocatalytic reaction
A single chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same or a coupled reaction.Steinfeld J.I., Francisco J.S. and Hase W.L. ''Chemical Kinetics and Dynamics'' (2nd ed., Prentice-Hall 199 ...
.
The Brusselator model was proposed by
Ilya Prigogine
Viscount Ilya Romanovich Prigogine (; russian: Илья́ Рома́нович Приго́жин; 28 May 2003) was a physical chemist and Nobel laureate noted for his work on dissipative structures, complex systems, and irreversibility.
Biogra ...
and his collaborators at the
Université Libre de Bruxelles.
It is a portmanteau of
Brussels
Brussels (french: Bruxelles or ; nl, Brussel ), officially the Brussels-Capital Region (All text and all but one graphic show the English name as Brussels-Capital Region.) (french: link=no, Région de Bruxelles-Capitale; nl, link=no, Bruss ...
and
oscillator
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
.
It is characterized by the reactions
:
:
:
:
Under conditions where A and B are in vast excess and can thus be modeled at constant concentration, the rate equations become
:
:
where, for convenience, the rate constants have been set to 1.
The Brusselator has a fixed point at
:
:
.
The fixed point becomes unstable when
:
leading to an oscillation of the system. Unlike the
Lotka–Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially. Instead, after sufficient time, the oscillations approach a
limit cycle.
The best-known example is the
clock reaction
A chemical clock (or clock reaction) is a complex mixture of reacting chemical compounds in which the onset of an observable property (discoloration or coloration) occurs after a predictable induction time due to the presence of clock species at a ...
, the
Belousov–Zhabotinsky reaction (BZ reaction). It can be created with a mixture of potassium bromate
, malonic acid
, and manganese sulfate
prepared in a heated solution of sulfuric acid
.
BZ reaction
See also
* Lotka–Volterra equation
* Oregonator
References
{{reflist
Non-equilibrium thermodynamics
Chaotic maps
Oscillators
Ordinary differential equations