Modelirovanie i Analiz Informatsionnykh Sistem
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Model. Anal. Inform. Sist.:
Year:
Volume:
Issue:
Page:
Find






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


Modelirovanie i Analiz Informatsionnykh Sistem, 2013, Volume 20, Number 5, Pages 25–44 (Mi mais330)  

This article is cited in 1 scientific paper (total in 1 paper)

Features of Oscillations in Adiabatic Oscillators with Delay

P. N. Nesterov, E. N. Agafonchikov

P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia
Full-text PDF (786 kB) Citations (1)
References:
Abstract: In this paper, we describe the features of oscillations in adiabatic oscillators when the delay is introduced into the equation. We give a short description of the method of asymptotic integration of one class of linear delay differential systems in the neighborhood of infinity. This method is based on the idea of transforming the initial system in order to reduce it to the system that is close in some sense to the system of ordinary differential equations. When applying this method, we need to extend the phase space of the initial system. The averaging changes of variables are also used to simplify the procedure of constructing the asymptotic formulas. Finally, we apply the functional differential analog of the Levinson theorem. We use this method to get the asymptotic formulas for adiabatic oscillators with delay under a monotonely and also oscillatory tending to zero perturbations. In conclusion, we study the transformation of the parametric resonance zone of one adiabatic oscillator when the delay is varied.
Keywords: adiabatic oscillator, delay differential equation, resonance, method of averaging, asymptotics.
Received: 14.08.2013
Document Type: Article
UDC: 517.929
Language: Russian
Citation: P. N. Nesterov, E. N. Agafonchikov, “Features of Oscillations in Adiabatic Oscillators with Delay”, Model. Anal. Inform. Sist., 20:5 (2013), 25–44
Citation in format AMSBIB
\Bibitem{NesAga13}
\by P.~N.~Nesterov, E.~N.~Agafonchikov
\paper Features of Oscillations in Adiabatic Oscillators with Delay
\jour Model. Anal. Inform. Sist.
\yr 2013
\vol 20
\issue 5
\pages 25--44
\mathnet{http://mi.mathnet.ru/mais330}
Linking options:
  • https://www.mathnet.ru/eng/mais330
  • https://www.mathnet.ru/eng/mais/v20/i5/p25
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Моделирование и анализ информационных систем
    Statistics & downloads:
    Abstract page:237
    Full-text PDF :98
    References:51
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024