One More Thing on the Subject: Generating Chaos via x | x | a −1, Melnikov’s Approach Using Simulations

Nikolay Kyurkchiev, 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
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, 1-11

Abstract: In this article, we propose a new hypothetical differential model with many free parameters, which makes it attractive to users. The motivation is as follows: an extended model is proposed that allows us to investigate classical and newer models appearing in the literature at a “higher energy level”, as well as the generation of high–order Melnikov polynomials (corresponding to the proposed extended model) with possible applications in the field of antenna feeder technology. 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.

Keywords: generating chaos via x | x | a ?1; Melnikov’s approach; Melnikov antenna factor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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