Controlling chaos in the Belousov—Zhabotinsky reaction

Petrov, Valery; Gáspár, Vilmos; Masere, Jonathan; Showalter, Kenneth

doi:10.1038/361240a0

Cited by 408Chaos control and synchronizationNonlinear Dynamics and Pattern FormationMathematical Dynamics and Fractals

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Controlling chaos in the Belousov—Zhabotinsky reaction

Petrov, Valery, Gáspár, Vilmos, Masere, Jonathan, Showalter, Kenneth·1993·Nature

DOI 10.1038/361240a0

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GARD composomes portray a special type of self-organization, different from the typical spatio-temporal patterns seen in experimental models in inorganic chemistry or physics.
“GARD composomes portray a special type of self-organization, different from the typical spatio-temporal patterns seen in experimental models in the realms of inorganic chemistry (Belousov–Zhabotinsky reactions [141]) or physics (Benard cells [142]).”
From Systems protobiology: origin of life in lipid catalytic networks (2018) · cites this paper as [141]

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Ott, E., Grebogi, C., & Yorke, J. A. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.1196 · Cited by 5,431
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Ditto, W. L., Rauseo, S. N., & Spano, M. L. (1990) · Physical Review Letters · doi:10.1103/physrevlett.65.3211 · Cited by 713
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Hunt, E. R. (1991) · Physical Review Letters · doi:10.1103/physrevlett.67.1953 · Cited by 639
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Controlling a chaotic system
Singer, J., Wang, Y.-Z., & Bau, H. H. (1991) · Physical Review Letters · doi:10.1103/physrevlett.66.1123 · Cited by 350
Mixed-mode oscillations in chemical systems
Petrov, V., Scott, S. K., & Showalter, K. (1992) · The Journal of Chemical Physics · doi:10.1063/1.463727 · Cited by 237
Self-citation
One-Dimensional Dynamics in a Multicomponent Chemical Reaction
Simoyi, R. H., Wolf, A., & Swinney, H. L. (1982) · Physical Review Letters · doi:10.1103/physrevlett.49.245 · Cited by 224
Controlling chemical chaos
Peng, B., Petrov, V., & Showalter, K. (1991) · The Journal of Physical Chemistry · doi:10.1021/j100166a013 · Cited by 210
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Simoyi, R. H., Wolf, A., & Swinney, H. L. (2017) · CRC Press eBooks · doi:10.1201/9780203734636-14 · Cited by 173
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Györgyi, L., & Field, R. J. (1992) · Nature · doi:10.1038/355808a0 · Cited by 133
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Self-citation
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Coffman, K., McCormick, W. D., Noszticzius, Z., Simoyi, R. H., & Swinney, H. L. (1987) · The Journal of Chemical Physics · doi:10.1063/1.452603 · Cited by 67
Effect of trace impurities on a bifurcation structure in the Belousov-Zhabotinskii reaction: preparation of high-purity malonic acid
Noszticzius, Z., McCormick, W. D., & Swinney, H. L. (1987) · The Journal of Physical Chemistry · doi:10.1021/j100303a051 · Cited by 41
Quenching of chemical oscillations
Hynne, F., & Soerensen, P. G. (1987) · The Journal of Physical Chemistry · doi:10.1021/j100311a002 · Cited by 29
Amplitudes and phases of small-amplitude Belousov-Zhabotinskii oscillations derived from quenching experiments
Soerensen, P. G., & Hynne, F. (1989) · The Journal of Physical Chemistry · doi:10.1021/j100351a030 · Cited by 25
Experimental study of embedding of attractors in concentration space
Sørensen, P. G., Hynne, F., & Nielsen, K. (1990) · Reaction Kinetics and Catalysis Letters · doi:10.1007/bf02065365 · Cited by 4

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Experimental Maintenance of Chaos
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Chaos : Its significance and detection in biology
Lloyd, A. L., & Lloyd, D. (1995) · Biological Rhythm Research · doi:10.1080/09291019509360338 · Cited by 62
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Boccaletti, S., & Arecchi, F. T. (1995) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/31/3/001 · Cited by 62
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Photo-response of chemical oscillators
Hanazaki, I., Mori, Y., Sekiguchi, T., & RABAI, G. (1995) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(95)00028-3 · Cited by 44
Encoding information in chemical chaos by controlling symbolic dynamics
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Authors: Petrov, V., Gáspár, V., Masere, J., & Showalter, K.
Affiliations: West Virginia University (US)
ORCID: Gáspár, Vilmos
Showalter, Kenneth
Venue: Nature
Publisher: Springer Science and Business Media LLC
Published: 1993-01
Volume: 361
Issue: 6409
Pages: 240-243
ISSN: 0028-0836 (ISSN-L)
1476-4687
DOI: 10.1038/361240a0
OpenAlex: W2030991498
Cited by: 408
References: 17
Citations by year: 2026: 11 · 2025: 4 · 2024: 10 · 2023: 10 · 2022: 11 · 2021: 10 · 2020: 13 · 2019: 8 · 2018: 8 · 2017: 10 · 2016: 26 · 2015: 13 · 2014: 13 · 2013: 4 · 2012: 9
FWCI: 20.34
Type: journal article
Language: en
Open access: closed
Licence: www.springer.com/tdm (tdm)
Locations: Nature (publishedVersion)
University of Debrecen Electronic Archive (University of Debrecen) (submittedVersion)
Topics: Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Dynamics and Pattern Formation
Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
Keywords: chaos control, Belousov-Zhabotinsky reaction, deterministic chaos, feedback control, proportional control, periodic oscillations, sensitivity to initial conditions

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