ODE model of autocatalytic reaction
The Oregonator is a theoretical model for a type of autocatalytic reaction .
The Oregonator is the simplest realistic model of the chemical dynamics of the oscillatory Belousov–Zhabotinsky reaction .[ 1] Richard M. Noyes at the University of Oregon .[ 2] Oregon and oscillator .
Earlier, the Brusselator model was proposed by Ilya Prigogine and his collaborators at the Free University of Brussels [ 3] Brussels and oscillator .
The Oregonator is a reduced model of the FKN mechanism (developed by Richard Field, Endre Kőrös , and Richard M. Noyes ) which still involved 11 reactions and 12 species (21 intermediate species and 18 elementary steps). The Oregonator is characterized by the reactions[ note 1]
I
A
+
Y
⟶
X
+
P
II
X
+
Y
⟶
2
P
III
A
+
X
⟶
2
X
+
2
Z
IV
2
X
⟶
A
+
P
V
B
+
Z
⟶
1
2
f
Y
d
[
X
]
d
t
=
k
I
[
A
]
[
Y
]
−
k
I
I
[
X
]
[
Y
]
+
k
I
I
I
[
A
]
[
X
]
−
2
k
I
V
[
X
]
2
d
[
Y
]
d
t
=
−
k
I
[
A
]
[
Y
]
−
k
I
I
[
X
]
[
Y
]
+
1
2
f
k
V
[
B
]
[
Z
]
d
[
Z
]
d
t
=
2
k
I
I
I
[
A
]
[
X
]
−
k
V
[
B
]
[
Z
]
{\displaystyle {\begin{aligned}{\text{I}}\quad &A+Y\longrightarrow X+P\\[5pt]{\text{II}}\quad &X+Y\longrightarrow 2P\\[5pt]{\text{III}}\quad &A+X\longrightarrow 2X+2Z\\[5pt]{\text{IV}}\quad &2X\longrightarrow A+P\\[5pt]{\text{V}}\quad &B+Z\longrightarrow {\frac {1}{2}}fY\\[5pt]&{\frac {d[X]}{dt}}=k_{I}[A][Y]-k_{II}[X][Y]+k_{III}[A][X]-2k_{IV}[X]^{2}\\[5pt]&{\frac {d[Y]}{dt}}=-k_{I}[A][Y]-k_{II}[X][Y]+{\frac {1}{2}}fk_{V}[B][Z]\\[5pt]&{\frac {d[Z]}{dt}}=2k_{III}[A][X]-k_{V}[B][Z]\end{aligned}}}
See also
Notes
^ The mechanism below as well as the rate equations are from the Scholarpedia article.[ 1] [ 2]
References
![{\displaystyle {\begin{aligned}{\text{I}}\quad &A+Y\longrightarrow X+P\\[5pt]{\text{II}}\quad &X+Y\longrightarrow 2P\\[5pt]{\text{III}}\quad &A+X\longrightarrow 2X+2Z\\[5pt]{\text{IV}}\quad &2X\longrightarrow A+P\\[5pt]{\text{V}}\quad &B+Z\longrightarrow {\frac {1}{2}}fY\\[5pt]&{\frac {d[X]}{dt}}=k_{I}[A][Y]-k_{II}[X][Y]+k_{III}[A][X]-2k_{IV}[X]^{2}\\[5pt]&{\frac {d[Y]}{dt}}=-k_{I}[A][Y]-k_{II}[X][Y]+{\frac {1}{2}}fk_{V}[B][Z]\\[5pt]&{\frac {d[Z]}{dt}}=2k_{III}[A][X]-k_{V}[B][Z]\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7c5040dd3ed2575026696bc7dba4459c08877916)