Oregonator

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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.[1] 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[2] 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

  1. ↑ "Oregonator". Retrieved 2010-05-16. 
  2. ↑ "IDEA - Internet Differential Equations Activities". Washington State University. Retrieved 2010-05-16. 
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