Highly structured ring spectrum

The Oregonator is a theoretical model for a type of autocatalytic reaction. The Oregonator (Orygunator) is the simplest realistic model of the chemical dynamics of the oscillatory Belousov-Zhabotinsky reaction. It was created by Richard M. Noyes at the University of Oregon. It is a portmanteau of Oregon and oscillator.

Earlier, the Brusselator model was proposed by Ilya Prigogine and his collaborators at the Free University of Brussels as a portmanteau of Brussels and oscillator.

The Oregonator is characterized by the reactions

I		A + Y	$\longrightarrow$	X + P
II		X + Y	$\longrightarrow$	2 P
III		A + X	$\longrightarrow$	2 X + 2 Z
IV		2 X	$\longrightarrow$	A + P
V		B + Z	$\longrightarrow$	f Y

${\frac {d[X]}{dt}}=k_{I}[A][Y]-k_{II}[X][Y]+k_{III}[A][X]-2k_{IV}[X]^{2}$

${\frac {d[Y]}{dt}}=-k_{I}[A][Y]-k_{II}[X][Y]+{\frac {1}{2}}fk_{V}[B][Z]$

${\frac {d[Z]}{dt}}=2k_{III}[A][X]-k_{V}[B][Z]$

density curves of Oregonator

Limit cycle of Orgegonator in 3D phase space

See also

• Lotka-Volterra equation

References

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