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Dynamics of a Class of Chemical Oscillators with Asymmetry Potential: Simulations and Control over Oscillations

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  • Nikolay Kyurkchiev

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria
    Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria)

  • Tsvetelin Zaevski

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria
    Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 5, James Bourchier Blvd., 1164 Sofia, Bulgaria)

  • Anton Iliev

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria)

  • Vesselin Kyurkchiev

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria)

  • Asen Rahnev

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria)

Abstract

The literature devoted to the issue of a forced modified Van der Pol–Duffing oscillator with asymmetric potential is a major and varied way to represent nonlinear dissipative chemical dynamics. It is known that this model is based on the real reaction–kinetic scheme. In this paper, we suggest a novel class of oscillators that are appealing to users due to their numerous free parameters and asymmetric potential. The rationale for this is because an expanded model is put out that enables the investigation of both classical and more recent models that have been reported in the literature at a “higher energy level”. We present a few specific modules for examining these oscillators’ behavior. A much broader Web-based application for scientific computing will incorporate this as a key component. Probabilistic construction to offer possible control over the oscillations is also considered.

Suggested Citation

  • Nikolay Kyurkchiev & Tsvetelin Zaevski & Anton Iliev & Vesselin Kyurkchiev & Asen Rahnev, 2025. "Dynamics of a Class of Chemical Oscillators with Asymmetry Potential: Simulations and Control over Oscillations," Mathematics, MDPI, vol. 13(7), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1129-:d:1623650
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    References listed on IDEAS

    as
    1. Nikolay Kyurkchiev & Anton Iliev & Vesselin Kyurkchiev & Asen Rahnev, 2025. "One More Thing on the Subject: Generating Chaos via x | x | a −1 , Melnikov’s Approach Using Simulations," Mathematics, MDPI, vol. 13(2), pages 1-11, January.
    2. Yan Zhang & Jin Zhang, 2024. "Existence of a Global Attractor for the Reaction–Diffusion Equation with Memory and Lower Regularity Terms," Mathematics, MDPI, vol. 12(21), pages 1-10, October.
    3. Malik Zaka Ullah & Ramandeep Behl & Ioannis K. Argyros, 2020. "Some High-Order Iterative Methods for Nonlinear Models Originating from Real Life Problems," Mathematics, MDPI, vol. 8(8), pages 1-17, July.
    4. Alicia Cordero & Moin-ud-Din Junjua & Juan R. Torregrosa & Nusrat Yasmin & Fiza Zafar, 2018. "Efficient Four-Parametric with-and-without-Memory Iterative Methods Possessing High Efficiency Indices," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-12, April.
    5. Nikolay Kyurkchiev & Tsvetelin Zaevski & Anton Iliev & Vesselin Kyurkchiev & Asen Rahnev, 2025. "Investigations of Modified Classical Dynamical Models: Melnikov’s Approach, Simulations and Applications, and Probabilistic Control of Perturbations," Mathematics, MDPI, vol. 13(2), pages 1-21, January.
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