Abstract
DETERMINISTIC chaos is characterized by long-term unpredictability arising from an extreme sensitivity to initial conditions. Such behaviour may be undesirable, particularly for processes dependent on temporal regulation. On the other hand, a chaotic system can be viewed as a virtually unlimited reservoir of periodic behaviour which may be accessed when appropriate feedback is applied to one of the system parameters1. Feedback algorithms have now been successfully applied to stabilize periodic oscillations in chaotic laser2, diode3, hydrodynamic4 and magnetoelastic5 systems, and more recently in myocardial tissue6. Here we apply a map-based, proportional-feedback algorithm7,8 to stabilize periodic behaviour in the chaotic regime of an oscillatory chemical system: the Belousov–Zhabotinsky reaction.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Ott, E., Grebogi, C. & Yorke, J. A. Phys. Rev. Lett. 64, 1196–1199 (1990).
Roy, R., Murphy, T. W., Maier, T. D., Gills, Z. & Hunt, E. R. Phys. Rev. Lett. 68, 1259–1262 (1992).
Hunt, E. R. Phys. Rev. Lett. 67, 1953–1955 (1991).
Singer, J., Wang, Y-Z. & Bau, H. H. Phys. Rev. Lett. 66, 1123–1125 (1991).
Ditto, W. L., Rauseo, S. N. & Spano, M. L. Phys. Rev. Lett. 65, 3211–3214 (1990).
Garfinkel, A., Spano, M. L., Ditto, W. L. & Weiss, J. N. Science 257, 1230–1235 (1992).
Peng, B., Petrov, V. & Showalter, K. J. phys. Chem. 95, 4957–4959 (1991).
Petrov, V., Peng, B. & Showalter, K. J. chem. Phys. 96, 7506–7513 (1992).
Simoyi, R. H., Wolf, A. & Swinney, H. L. Phys. Rev. Lett. 49, 245–248 (1982).
Coffmann, K. G., McCormick, W. D., Noszticzius, Z., Simoyi, R. H. & Swinney, H. L. J. chem. Phys. 86, 119–129 (1987).
Noszticzius, Z., McCormick, W. D. & Swinney, H. L. J. phys. Chem. 91, 5129–5134 (1987).
Györgyi, L. & Field, R. J. Nature 355, 808–810 (1992).
Hynne, F. & Sørensen, P. G. J. phys. Chem. 91, 6573–6575 (1987).
Sørensen, P. G. & Hynne, F. J. phys. Chem. 93, 5467–5474 (1989).
Sørensen, P. G., Hynne, F. & Nielsen, K. Reaction Kinet. Catal. Lett. 42, 309–315 (1990).
Doedel, E. AUTO: Software for Continuation and Bifurcation Problems in Ordinary Differential Equations (Applied Mathematics, California Institute of Technology, Pasadena, 1986).
Petrov, V., Scott, S. K. & Showalter, K. J. chem. Phys. 97, 6191–6198 (1992).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Petrov, V., Gáspár, V., Masere, J. et al. Controlling chaos in the Belousov—Zhabotinsky reaction. Nature 361, 240–243 (1993). https://doi.org/10.1038/361240a0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/361240a0
This article is cited by
-
Automatically discovering ordinary differential equations from data with sparse regression
Communications Physics (2024)
-
A programmable hybrid digital chemical information processor based on the Belousov-Zhabotinsky reaction
Nature Communications (2024)
-
A computational approach for the generalised Genesio–Tesi systems using a novel fractional operator
Pramana (2024)
-
Evaluating the nonlinear behavior of tall buildings with end shear walls through chaos theory
Innovative Infrastructure Solutions (2024)
-
Non-autonomous zinc–methylimidazole oscillator and the formation of layered precipitation structures in a hydrogel
Scientific Reports (2023)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.
