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Dynamics of a Forced Brusselator

​
time t
400.
​
forcing amplitude f
0.05
parameter a
0.4
forcing frequency ω
0.81
parameter b
1.2
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
AX;B+XY+D;2X+Y3X;XE
. The model describes a chemical system that converts reactant
A
to a final product
E
through four steps. For simplicity, the concentrations
a
and
b
of
A
and
B
are maintained constant, and all reaction rates are set equal to one. The system of differential equations that describe the dimensionless concentrations
x
and
y
of species
X
and
Y
in the forced Brusselator are
x
=a+
2
x
y-(b+1)x+fcos(ωt)
and
y
=bx-a
2
x
y
, where
f
is the force amplitude and
ω
is the force frequency. You can vary the parameters
a
,
b
,
f
, and
ω
to see the trajectories of the variables
x
and
y
.
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