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

Nikolay Kyurkchiev, Tsvetelin Zaevski, Anton Iliev (), Vesselin Kyurkchiev and Asen Rahnev
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Nikolay Kyurkchiev: Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria
Tsvetelin Zaevski: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 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

Mathematics, 2025, vol. 13, issue 2, 1-21

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.

Keywords: extended classical oscillators; Melnikov’s approach; antenna factor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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