Dynamics of a Forced Brusselator

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This Demonstration shows the dynamics of a forced Brusselator model. The Brusselator is an example of an autocatalytic chemical reaction. The model can represent a limit cycle, Andronov–Hopf bifurcation, and also chaotic behavior when a sinusoidal force acts on the system [1]. This force could be heat convection, microwave radiation, or some other force that varies sinusoidally with small intensity.


The chemical reactions of the Brusselator are . The model describes a chemical system that converts reactant to a final product through four steps. For simplicity, the concentrations and of and are maintained constant, and all reaction rates are set equal to one. The system of differential equations that describe the dimensionless concentrations and of species and in the forced Brusselator are and , where is the force amplitude and is the force frequency. You can vary the parameters , , , and to see the trajectories of the variables and .


Contributed by: Clay Gruesbeck (July 2015)
Open content licensed under CC BY-NC-SA




[1] A. Sanayei, "Controlling Chaotic Forced Brusselator Chemical Reaction," Proceedings of the World Congress on Engineering 2010 (WCE 2010), Vol. III, June 30–July 2, 2010, London, UK. www.iaeng.org/publication/WCE2010/WCE2010_pp1917-1922.pdf.

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