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Investigations of Modified Classical Dynamical Models: Melnikov’s Approach, Simulations and Applications, and Probabilistic Control of Perturbations

Author

Listed:
  • 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

We suggest a few kinds of extended classical oscillators in this study. We present a few specific modules for examining these oscillators’ behavior. This will be an essential component of a broader web-based scientific computing platform that is in the works. The modeling and synthesis of radiating antenna designs is also taken into consideration as a potential use case for Melnikov functions. Additionally, we discuss strategies for achieving probabilistic control over system perturbations.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:231-:d:1564832
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