Abstract
The article describes results of the modified model of the Belousov-Zhabotinsky reaction which resembles well the limit set observed in an experiment in the Petri dish. We discuss the concept of the ignition of circular waves and show that only an asymmetrical ignition leads to the formation of spiral structures. From the qualitative assumptions on the behavior of dynamic systems we conclude that the reactants in the Belousov-Zhabotinsky reaction likely forms a regular grid.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Belousov, B.P.: Collection of Short Papers on Radiation Medicine, p. 145. Medical Publications, Moscow (1959)
Zhabotinsky, A.M.: Periodical process of oxidation of malonic acid solution (a study of the Belousov reaction kinetics). Biofizika 9, 306–311 (1964)
Zhabotinsky, A.M.: Periodic liquid phase reactions. Proc. Ac. Sci. USSR 157, 392–395 (1964)
Rovinsky, A.B., Zhabotinsky, A.M.: Mechanism and mathematical model of the oscillating bromate-ferroin-bromomalonic acid reaction. J. Phys. Chem. 88, 6081–6084 (1984)
Hagelstein, M., Liu, T., Mangold, S., Bauer, M.: Time-resolved combined XAS and UV-Vis applied to the study of the cerium catalysed BZ reaction. J. Phys. Conf. Ser. 430, 012123 (2013)
Vanag, V.K., Epstein, I.R.: Cross-diffusion and pattern formation in reaction-diffusion systems. Phys. Chem. Chem. Phys. 11, 897–912 (2009)
Gerhardt, M., Schuster, H.: A cellular automaton describing the formation of spatially ordered structures in chemical systems. Phys. D 36, 209–222 (1989)
Dewdney, A.K.: The hodgepodge machine makes waves. Sci. Am. 225, 104 (1988)
Wuensche, A.: Exploring Discrete Dynamics. Luniver Press, Frome (2011)
Wilensky, U.: NetLogo B-Z Reaction Model. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL (2003). http://ccl.northwestern.edu/netlogo/models/B-ZReaction
Zhyrova, A., Stys, D.: Construction of the phenomenological model of Belousov-Zhabotinsky reaction state trajectory. Int. J. Comput. Math. 91(1), 4–13 (2014)
Turing, A.M.: The chemical basis of morphogenesis. Philos. Trans. Roy. Soc. London 237, 37–72 (1952)
Bendixson, I.: Sur les courbes définies par des équations différentielles. Acta Math. 24, 1–88 (1901)
Fisch, R., Gravner, J., Griffeath, D.: Threshold-range scaling of excitable cellular automata. Stat. Comput. 1, 23–39 (1991)
Acknowledgments
This work was financially supported by CENAKVA (No. CZ.1.05/2.1.00/01.0024), CENAKVA II (No. LO1205 under the NPU I program) and The CENAKVA Centre Development (No. CZ.1.05/2.1.00/19.0380). Authors thank to Petr Jizba and Jaroslav Hlinka for important discussions and to Kaijia Tian for edits.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Štys, D., Náhlík, T., Zhyrova, A., Rychtáriková, R., Papáček, Š., Císař , P. (2016). Model of the Belousov-Zhabotinsky Reaction. In: Kozubek, T., Blaheta, R., Šístek, J., Rozložník, M., Čermák, M. (eds) High Performance Computing in Science and Engineering. HPCSE 2015. Lecture Notes in Computer Science(), vol 9611. Springer, Cham. https://doi.org/10.1007/978-3-319-40361-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-40361-8_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40360-1
Online ISBN: 978-3-319-40361-8
eBook Packages: Computer ScienceComputer Science (R0)