Vestnik KRAUNC. Fiziko-Matematicheskie Nauki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestnik KRAUNC. Fiz.-Mat. Nauki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestnik KRAUNC. Fiziko-Matematicheskie Nauki, 2024, Volume 47, Number 2, Pages 21–34
DOI: https://doi.org/10.26117/2079-6641-2024-47-2-21-34
(Mi vkam644)
 

MATHEMATICAL MODELING

Mathematical model of Van der Pol-Airy fractional oscillator

A. I. Salimovaa, R. I. Parovikab

a National University of Uzbekistan named after M. Ulugbek, Tashkent
b Institute of Cosmophysical Researches and Radio Wave Propagation, Far East Division, Russian Academy of Sciences
References:
Abstract: The paper proposes a mathematical model of the nonlinear Van der Pol-Airy oscillator taking into account heredity. The nonlinearity of the oscillator is due to the dependence of the friction coefficient on the square of the displacement function, which is typical for the Van der Pol oscillator. Also, the natural frequency of oscillations is a function of time, which increases linearly as it increases. The latter is typical for the Airy oscillator. Heredity effects are introduced into the model equation through fractional derivatives in the Gerasimov-Caputo sense. They indicate that the oscillatory system may have memory effects that manifest themselves depending on its current state from previous ones. For the proposed mathematical model, a numerical algorithm was developed based on an explicit first-order finite-difference scheme. The numerical algorithm was implemented in a computer program in the Maple language, with the help of which the simulation results were visualized. Oscillograms and phase trajectories were constructed for various values of the model parameters. It is shown that a fractional mathematical model can have various oscillatory modes: from self-oscillatory, damped and chaotic. An interpretation of the simulation results is given
Keywords: mathematical model, Gerasimov-Caputo fractional derivative, oscillogram, phase trajectory, limit cycle, numerical algorithm.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 124012300245-2
The name of the funding programme: Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences (registration No. 124012300245-2).
Document Type: Article
UDC: 517.925.5
MSC: Primary 26A33; Secondary 34A08
Language: Russian
Citation: A. I. Salimova, R. I. Parovik, “Mathematical model of Van der Pol-Airy fractional oscillator”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 47:2 (2024), 21–34
Citation in format AMSBIB
\Bibitem{SalPar24}
\by A.~I.~Salimova, R.~I.~Parovik
\paper Mathematical model of Van der Pol-Airy fractional oscillator
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2024
\vol 47
\issue 2
\pages 21--34
\mathnet{http://mi.mathnet.ru/vkam644}
\crossref{https://doi.org/10.26117/2079-6641-2024-47-2-21-34}
Linking options:
  • https://www.mathnet.ru/eng/vkam644
  • https://www.mathnet.ru/eng/vkam/v47/i2/p21
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Vestnik KRAUNC. Fiziko-Matematicheskie Nauki Vestnik KRAUNC. Fiziko-Matematicheskie Nauki
    Statistics & downloads:
    Abstract page:6
    Full-text PDF :1
    References:4
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024