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Chaos Synchronization of Two Györgyi–Field Systems for the Belousov–Zhabotinsky Chemical Reaction

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  • Andrei Victor Oancea

    (Petru Poni Institute of Macromolecular Chemistry, 41A Grigore Ghica Voda Alley, 700487 Iasi, Romania)

  • Ilie Bodale

    (Department of Sciences, “Ion Ionescu de la Brad” Iasi University of Life Sciences, 3 M. Sadoveanu Alley, 700440 Iasi, Romania)

Abstract

Chemical reactions with oscillating behavior can present a chaos state in specific conditions. In this study, we analyzed the dynamic of the chaotic Belousov–Zhabotinsky (BZ) reaction using the Györgyi–Field model in order to identify the conditions of the chaos behavior. We studied the behavior of the reaction under different parameters that included both a low and high flux of chemical species. We performed our analysis of the flow regime in the conditions of an open reaction system, as this provides information about the behavior of the reaction over time. The proposed method for determining the favorable conditions for obtaining the state of chaos is based on the time evolution of the intermediate species and phase portraits. The synchronization of two Györgyi–Field systems based on the adaptive feedback method of control is presented in this work. The transient time until synchronization depends on the initial conditions of the two systems and on the strength of the controllers. Among the areas of interest for possible applications of the control method described in this paper, we can include identification of the reaction parameters and the extension to the other chaotic systems.

Suggested Citation

  • Andrei Victor Oancea & Ilie Bodale, 2022. "Chaos Synchronization of Two Györgyi–Field Systems for the Belousov–Zhabotinsky Chemical Reaction," Mathematics, MDPI, vol. 10(21), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:3947-:d:951723
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    References listed on IDEAS

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    1. Shepelev, I.A. & Vadivasova, T.E., 2021. "Synchronization in multiplex networks of chaotic oscillators with frequency mismatch," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Guo, Wanli & Chen, Shihua & Zhou, Hong, 2009. "A simple adaptive-feedback controller for chaos synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 316-321.
    3. Oancea, Servilia & Grosu, Florin & Lazar, Anca & Grosu, Ioan, 2009. "Master–slave synchronization of Lorenz systems using a single controller," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2575-2580.
    4. Bei Chen & Xinxin Cheng & Han Bao & Mo Chen & Quan Xu, 2022. "Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator," Mathematics, MDPI, vol. 10(5), pages 1-13, February.
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    Cited by:

    1. Karimov, Artur & Kopets, Ekaterina & Karimov, Timur & Almjasheva, Oksana & Arlyapov, Viacheslav & Butusov, Denis, 2023. "Empirically developed model of the stirring-controlled Belousov–Zhabotinsky reaction," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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