Oregonator

The Oregonator is, like the Brusselsator , a model for describing oscillating chemical reactions . It was proposed in 1972 by Richard J. Field, Endre Körös, and Richard M. Noyes of the University of Oregon to describe the Belousov-Zhabotinsky reaction . It got the name, based on the Brusselsator, because Fields et al. were working at the University of Oregon at the time (the name Brusselsator itself is a cross between the name of the city of Brussels and oscillator ). The Oregonator model is a reduced form of the FKN model , according to the initials of the authors, which still has 11 reactions with 12 chemical species.

The model

The Oregonator model consists of five reactions among seven chemical species {A, B, P, Q, X, Y, Z}:

I.		A + Y	${\displaystyle \longrightarrow }$	X
II		X + Y	${\displaystyle \longrightarrow }$	P
III		B + X	${\displaystyle \longrightarrow }$	2 X + Z
IV		2 X	${\displaystyle \longrightarrow }$	Q
V		Z	${\displaystyle \longrightarrow }$	f Y

The concentrations of species A and B are kept constant and the products P and Q are continuously removed, so that only three variables have to be taken into account. When f in ( V ) is another parameter (such as the concentration [A] and [B]).

The rate equations result :

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

${\displaystyle {\frac {\mathrm {d} [Y]}{\mathrm {d} t}}=-k_{\mathrm {I} }[A][Y]-k_{\mathrm {II} }[X][Y]+fk_{\mathrm {V} }[Z]}$

${\displaystyle {\frac {\mathrm {d} [Z]}{\mathrm {d} t}}=k_{\mathrm {III} }[B][X]-k_{\mathrm {V} }[Z]}$

literature

• James D. Murray : Mathematical Biology I: An Introduction. 3rd ed. , Springer Science + Business Media, Inc, 2002.

Web links

• Scholarpedia article on Oregonator

swell

1. ↑ Richard J. Field, Endre Körös, Richard M. Noyes (1972): Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system J. Am. Chem. Soc. 94 (25), pp. 8649-8664, doi : 10.1021 / ja00780a001 .
2. ↑ Richard J. Field, Richard M. Noyes (1974): Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction J. Chem. Phys. 60, pp. 1877-1884, doi : 10.1063 / 1.1681288 .
3. ↑ Herrmann Haken: Synergetics; an introduction 3rd edition, Springer Verlag, 1990.