Dynamics of a Class of Extended Duffing–Van Der Pol Oscillators: Melnikov’s Approach, Simulations, Control over Oscillations

Nikolay Kyurkchiev, Tsvetelin Zaevski, Maria Vasileva, Vesselin Kyurkchiev, Anton Iliev () and Asen Rahnev
Additional contact information
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
Maria Vasileva: 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
Anton Iliev: 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 14, 1-21

Abstract: The Duffing–van der Pol oscillator is a very prominent and interesting standard model. There is a substantial body of varied literature on this topic. In this article, we propose a new class of oscillators by adding new factors to its dynamics. Investigations in light of Melnikov’s approach are considered. Several simulations are composed. A few specialized modules for testing the dynamics of the hypothetical oscillator under consideration are also given. This will be an essential component of a much broader Web-based scientific computing application that is planned. Possible control over oscillations: approximation with restrictions is also discussed; some probabilistic constructions are also presented.

Keywords: extended oscillator based on Duffing–van der Pol oscillator; Melnikov’s approach; control over oscillations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/14/2240/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/14/2240/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:14:p:2240-:d:1699112

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().