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

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)

  • 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

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.

Suggested Citation

  • Nikolay Kyurkchiev & Anton Iliev & Vesselin Kyurkchiev & Asen Rahnev, 2025. "One More Thing on the Subject: Generating Chaos via x | x | a −1 , Melnikov’s Approach Using Simulations," Mathematics, MDPI, vol. 13(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:232-:d:1564909
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