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WOLFRAM|DEMONSTRATIONS PROJECT

Oregonator with Time Delay

​
maximum time
30
delay time
0
parameter f
0.5
This Demonstration shows how time delay can change the stability of steady or oscillatory Oregonator model states, causing further oscillations or significantly altering existing ones and hence inducing delay-controlled periodic behavior.
From a chemical viewpoint, time delay could cause a stable equilibrium to become unstable and cause the properties in an Oregonator model to fluctuate. The equations describing the Oregonator model with delay are [1]
ϵ
dx
dτ
=qy-xy+x(1-x)
,
δ
dy
dτ
=-qy-xy+fz
,
dz
dτ
=x-z+kz(t-τ)
,
with
x(0)=y(0)=1
, and
z(t≤τ)=1
,
where
t
is time,
x
is
HBrO
2
,
y
is
-
Br
,
z
is
​
4+
Ce
, and
τ
is a time delay. The parameters are
k=0.1
,
ϵ=4
-2
10
,
δ=4
-4
10
,
q=8
-4
10
, and
f∈[0.4,0.6]
.
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