This historical review of the development of the Oregonator model of the Belousov–Zhabotinsky reaction is based on a lecture Dick Field presented during IrvFest2015—Celebrating a founding father of chaos!, a meeting in commemoration of Irving R. Epstein’s 70th birthday. For Dick’s 80th birthday festschrift, we focus here on the five papers in the series named “Oscillations in chemical systems,” published in 1972 [Noyes et al., J. Am. Chem. Soc. 94, 1394–1395 (1972); Field et al., J. Am. Chem. Soc. 94, 8649–8664 (1972); Field and Noyes, Nature 237, 390–392 (1972)] and 1974 [Field and Noyes, J. Chem. Phys. 60, 1877–1884 (1974); Field and Noyes, J. Am. Chem. Soc. 96, 2001–2006 (1974)].

1.
R. M.
Noyes
,
R. J.
Field
, and
E.
Kőrös
, “
Oscillations in chemical systems. I. Detailed mechanism in a system showing temporal oscillations
,”
J. Am. Chem. Soc.
94
,
1394
1395
(
1972
).
2.
R. J.
Field
,
E.
Kőrös
, and
R. M.
Noyes
, “
Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system
,”
J. Am. Chem. Soc.
94
,
8649
8664
(
1972
).
3.
R. J.
Field
and
R. M.
Noyes
, “
Explanation of spatial band propagation in the Belousov reaction
,”
Nature
237
,
390
392
(
1972
).
4.
R. J.
Field
and
R. M.
Noyes
, “
Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction
,”
J. Chem. Phys.
60
,
1877
1884
(
1974
).
5.
R. J.
Field
and
R. M.
Noyes
, “
Oscillations in chemical systems. V. Quantitative explanation of band migration in the Belousov-Zhabotinskii reaction
,”
J. Am. Chem. Soc.
96
,
2001
2006
(
1974
).
6.
A similar scientific discussion at that time involved “Polywater,” a new form of water with peculiar properties (e.g., denser and freezing at a lower temperature than ordinary water). This belief resulted from the 1969 Science paper Structure of “Polywater.”48 Many following papers appeared and conferences were held supporting the existence of this new form of water, despite disbelief among a majority of the scientific community.49 In the end, “Polywater” was determined to be contaminated by silicates from the capillary tubes in which it was found.50,51
7.
P.
Glansdorff
and
I.
Prigogine
,
Thermodynamic Theory of Structure, Stability and Fluctuations
(
Wiley-Interscience
,
London
,
1971
).
8.
H.-G.
Busse
, “
Spatial periodic homogeneous chemical reaction
,”
J. Phys. Chem.
73
,
750
(
1969
).
9.
T. A.
Bak
,
Contributions to the Theory of Chemical Kinetics. A Study of the Connection Between Thermodynamics and Chemical Rate Processes
(
W. A. Benjamin, Inc.
,
New York
,
1963
).
10.
R.
Wegscheider
, “
Über simultane Gleichgewichte und die Beziehungen zwischen Thermodynamik und Reactionskinetik homogener Systeme (About simultaneous equilibria and the relationship between thermodynamics and reaction kinetics of homogeneous systems)
,”
Monatsh. Chem.
22
,
849
906
(
1901
).
11.
R. C.
Thompson
, “
Reduction of bromine(V) by cerium(III), manganese(II), and neptunium(V) in aqueous sulfuric acid
,”
J. Am. Chem. Soc.
93
,
7315
(
1971
).
12.
G. V.
Buxton
and
F. S.
Dainton
, “
The radiolysis of aqueous solutions of oxybromine compounds; the spectra and reactions of BrO and BrO2
,”
Proc. R. Soc. London, Ser. A
304
,
427
439
(
1968
).
13.
R. M.
Noyes
,
R. J.
Field
, and
R. C.
Thompson
, “
Mechanism of reaction of bromine(V) with weak one-electron reducing agents
,”
J. Am. Chem. Soc.
93
,
7315
7316
(
1971
).
14.
C. L.
Lee
and
M. W.
Lister
, “
The decomposition of aqueous sodium bromite
,”
Can. J. Chem.
49
,
2822
2826
(
1971
).
15.
R. H.
Betts
and
A. N.
Mackenzie
, “
Isotopic exchange reactions in the system bromine-bromate-hypobromous acid
,”
Can. J. Chem.
29
,
655
665
(
1951
).
16.
J. J.
Tyson
, “Quantitative account of oscillations, bistability, and traveling waves in the Belousov-Zhabotinskii reaction,” in Oscillations and Traveling Waves in Chemical Systems, edited by R. J. Field and M. Burger (John Wiley & Sons, New York, 1985), pp. 93–144.
17.
R. J.
Field
and
H.-D.
Försterling
, “
On the oxybromine chemistry rate constants with cerium ions in the Field-Körös-Noyes mechanism of the Belousov-Zhabotinskii reaction: The equilibrium HBrO2+BrO3+H+2BrO2+H2O
,”
J. Phys. Chem.
90
,
5400
5407
(
1986
).
18.
L.
Hegedűs
,
M.
Wittmann
,
Z.
Noszticzius
,
S.
Yan
,
A.
Sirimungkala
,
H.-D.
Försterling
, and
R. J.
Field
, “
HPLC analysis of complete BZ systems. Evolution of the chemical composition in cerium and ferroin catalysed batch oscillators: Experiments and model calculations
,”
Faraday Discuss.
120
,
21
38
(
2002
).
19.
D.
Edelson
,
R. J.
Field
, and
R. M.
Noyes
, “
Mechanistic details of the Belousov-Zhabotinskii oscillations
,”
Int. J. Chem. Kinet.
7
,
417
432
(
1975
).
20.
L.
Györgyi
and
R. J.
Field
, “
A three-variable model of deterministic chaos in the Belousov–Zhabotinsky reaction
,”
Nature
355
,
808
810
(
1992
).
21.
R. J.
Field
, “
Chaos in the Belousov-Zhabotinsky reaction
,”
Mod. Phys. Lett. B
29
,
1530015
(
2015
). Note: This article also appeared in Ref. 25.
22.
J. J.
Tyson
, “
Some further studies of nonlinear oscillations in chemical systems
,”
J. Chem. Phys.
58
,
3919
3930
(
1973
).
23.
J. J.
Tyson
and
P. C.
Fife
, “
Target patterns in a realistic model of the Belousov–Zhabotinskii reaction
,”
J. Chem. Phys.
73
,
2224
2237
(
1980
).
24.
J. J.
Tyson
, The Belousov-Zhabotinskii Reaction, Lecture Notes in Biomathematics Vol. 10 (Springer, Berlin, 1976).
25.
R. J.
Field
, “Chaos in the Belousov-Zhabotinsky reaction,” in Peregrinations from Physics to Phylogeny, Essays on the Occasion of Hao Bailin’s 80th Birthday, edited by K. K. Phua and M. Ge (World Scientific Press, Singapore, 2016), pp. 37–82.
26.
R. J.
Field
and
D.
Schuldberg
, “
Social-support moderated stress: A nonlinear dynamical model and the stress-buffering hypothesis
,”
Nonlinear Dyn. Psychol. Life Sci.
15
,
53
85
(
2011
).
27.
W.
Isaacson
,
The Code Breaker: Jennifer Doudna, Gene Editing, and the Future of the Human Race
(
Simon & Schuster
,
New York
,
2021
).
28.
A. N.
Zaikin
and
A. M.
Zhabotinsky
, “
Concentration wave propagation in two-dimensional liquid-phase self-oscillating system
,”
Nature
225
,
535
537
(
1970
).
29.
L.
Zaikina
, personal communication (2022).
30.
A. M.
Turing
, “
The chemical basis of morphogenesis
,”
Philos. Trans. R. Soc. London, Ser. B
237
,
37
72
(
1952
).
31.
N.
Tompkins
,
N.
Li
,
C.
Girabawe
,
M.
Heymann
,
G. B.
Ermentrout
,
I. R.
Epstein
, and
S.
Fraden
, “
Testing Turing’s theory of morphogenesis in chemical cells
,”
Proc. Natl. Acad. Sci. U.S.A.
111
,
4397
4402
(
2014
).
32.
S. G.
Sobel
,
H. M.
Hastings
, and
R. J.
Field
, “
Oxidation state of BZ reaction mixtures
,”
J. Phys. Chem. A
110
,
5
7
(
2006
).
33.
A. T.
Winfree
, The Geometry of Biological Time, Interdisciplinary Applied Mathematics Vol. 12 (Springer, New York, 2001).
34.
R. J.
Field
, “
Das experiment: Eine oszillierende reaktion (the experiment: An oscillating reaction)
,”
Chem. unserer Zeit
7
,
171
176
(
1973
).
35.
R.
Luther
, “
Räumliche Fortpflanzung chemischer Reaktionen (Spatial propagation of chemical reactions)
,”
Z. Elektrochem.
12
,
596
600
(
1906
). Note: English translation in Ref. 52.
36.
R. M.
Noyes
, “
A survey of studies of the reaction between permanganate and oxalate ions
,”
Trans. New York Acad. Sci.
13
,
314
316
(
1951
).
37.
H. M.
Hastings
,
R. J.
Field
,
S. G.
Sobel
, and
D.
Guralnick
, “
Oregonator scaling motivated by the Showalter–Noyes limit
,”
J. Phys. Chem. A
120
,
8006
8010
(
2016
).
38.
A. T.
Winfree
, “
Spiral waves of chemical activity
,”
Science
175
,
634
636
(
1972
).
39.
A.
Winfree
, “Stably rotating patterns of reaction and diffusion,” in Theoretical Chemistry (Elsevier, 1978), pp. 1–51.
40.
A. T.
Winfree
, “
Rotating chemical reactions
,”
Sci. Am.
230
,
82
95
(
1974
).
41.
J. P.
Keener
and
J. J.
Tyson
, “
Spiral waves in the Belousov-Zhabotinskii reaction
,”
Physica D
21
,
307
324
(
1986
).
42.
O. E.
Rössler
, “A synthetic approach to exotic kinetics (with examples),” in Physics and Mathematics of the Nervous System, edited by S. Levin, M. Conrad, W. Güttinger, and M. Dal Cin (Springer, Berlin, 1974), Vol. 4, pp. 546–582.
43.
R. J.
Field
and
A. T.
Winfree
, “
Travelling waves of chemical activity in the Zaikin-Zhabotinskii-Winfree reagent
,”
J. Chem. Educ.
56
,
754
(
1979
).
44.
P. G.
Bowers
,
K.
Bar-Eli
, and
R. M.
Noyes
, “
Unstable supersaturated solutions of gases in liquids and nucleation theory
,”
J. Chem. Soc. Faraday Trans.
92
,
2843
(
1996
).
45.
S. D.
Furrow
and
R. M.
Noyes
, “
The oscillatory Briggs-Rauscher reaction. 1. Examination of subsystems
,”
J. Am. Chem. Soc.
104
,
38
42
(
1982
).
46.
P. G.
Bowers
and
R. M.
Noyes
, “
Chemical oscillations and instabilities. 51. Gas evolution oscillators. 1. Some new experimental examples
,”
J. Am. Chem. Soc.
105
,
2572
2574
(
1983
).
47.
N.
Manz
, “History of the Belousov-Zhabotinsky reaction,” see http://woosterdigital.org/BZ-history (2022) (accessed January 22, 2022).
48.
J.
Donohue
, “
Structure of polywater
,”
Science
166
(
3908
),
1000
1002
(
1969
).
49.
A.
Ramirez
, “The rise and fall of polywater,” see https://www.sciencehistory.org/distillations/therise- and-fall-of-polywater (2020) (accessed January 22, 2022).
50.
R. E.
Davis
,
D. L.
Rousseau
, and
R. D.
Board
, “
Polywater: Evidence from electron spectroscopy for chemical analysis ESCA of a complex salt mixture
,”
Science
171
(
3967
),
167
170
(
1971
).
51.
D. L.
Rousseau
, “
Polywater and sweat: Similarities between the infrared spectra
,”
Science
171
(
3967
),
170
172
(
1971
).
52.
R.
Luther
, “
Propagation of chemical reactions in space
,”
J. Chem. Educ.
64
(
9
),
740
(
1987
). Note: English translation of his original German article35 by R. Arnold, K. Showalter, and J. J. Tyson (1987).
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