{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T15:04:04Z","timestamp":1778857444123,"version":"3.51.4"},"reference-count":61,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T00:00:00Z","timestamp":1710460800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this article, we propose some extended oscillator models. Various experiments are performed. The models are studied using the Melnikov approach. We show some integral units for researching the behavior of these hypothetical oscillators. These will be implemented as add-on sections of a thoughtful main web-based application for researching computations. One of the main goals of the study is to share the difficulties that researchers (who are not necessarily professional mathematicians) encounter in using contemporary computer algebraic systems (CASs) for scientific research to examine in detail the dynamics of modifications of classical and newer models that are emerging in the literature (for the large values of the parameters of the models). The present article is a natural continuation of the research in the direction that has been indicated and discussed in our previous investigations. One possible application that the Melnikov function may find in the modeling of a radiating antenna diagram is also discussed. Some probability-based constructions are also presented. We hope that some of these notes will be reflected in upcoming registered rectifications of the CAS. The aim of studying the design realization (scheme, manufacture, output, etc.) of the explored differential models can be viewed as not yet being met.<\/jats:p>","DOI":"10.3390\/a17030121","type":"journal-article","created":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T09:32:30Z","timestamp":1710495150000},"page":"121","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Modeling of Some Classes of Extended Oscillators: Simulations, Algorithms, Generating Chaos, and Open Problems"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0650-3285","authenticated-orcid":false,"given":"Nikolay","family":"Kyurkchiev","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria"},{"name":"Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1118-4189","authenticated-orcid":false,"given":"Tsvetelin","family":"Zaevski","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria"},{"name":"Faculty of Mathematics and Informatics, Sofia University \u201cSt. Kliment Ohridski\u201d, 5, James Bourchier Blvd., 1164 Sofia, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9796-8453","authenticated-orcid":false,"given":"Anton","family":"Iliev","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria"},{"name":"Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3559-182X","authenticated-orcid":false,"given":"Vesselin","family":"Kyurkchiev","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0381-2445","authenticated-orcid":false,"given":"Asen","family":"Rahnev","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1142\/S0218127499000523","article-title":"The effect of nonlinear damping on the universal oscillator","volume":"9","author":"Sanjuan","year":"1999","journal-title":"Int. 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