Brusselator

The Brusselator is a theoretical model for a type of autocatalytic reaction.

The Brusselator model was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles.

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.

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.

Top: The Brusselator in the unstable regime (A=1, B=3): The system approaches a limit cycle Bottom: The Brusselator in a stable regime with A=1 and B=1.7: For B<1+A 2 the system is stable and approaches a fixed point .
Simulation of the Brusselator as reaction diffusion system in two spatial dimensions
Simulation [ 1 ] of the reaction-diffusion system of the Brusselator with reflective border conditions