Radiophysics and Quantum Electronics

, Volume 61, Issue 8–9, pp 633–639 | Cite as

Asymptotic Behavior of the Solutions of a System of Two Weakly Coupled Relaxation Oscillators with Delayed Feedback

  • A. A. KashchenkoEmail author
  • S. A. Kaschenko

We consider a dynamic system that consists of two coupled self-excited oscillators with delayed feedback. Such models occur in applied problems of radio physics and optics. It is assumed that the nonlinear function, which is responsible for the feedback, is finite and contains a great parameter. This reveals the possibility to use a special analytical method to study relaxation oscillations. It is shown that the dynamics of two such oscillators in the case of their asymptotically weak coupling is described by a special finite-dimension mapping and can be rather sophisticated.


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  1. 1.
    V. Ya. Kislov and A. S. Dmitriev, Problems of Modern Radio Engineering and Electronics [in Russian], ed. by V. A. Kotelnikov, Nauka, Moscow (1987).Google Scholar
  2. 2.
    T. Kilias, K. Kelber, A. Mogel, et al., Intern. J. Electron., 79, No. 6, 737 (1995).CrossRefGoogle Scholar
  3. 3.
    A. S. Dmitriev and V. Ya. Kislov, Stochastic Oscillations in Radio Physics and Electronics [in Russian], Nauka, Moscow (1989).Google Scholar
  4. 4.
    J. Losson, M. C. Mackey, and A. Longtin, Chaos: An Interdisciplinary J. Nonlinear Science, 3, No. 2, 167 (1993).CrossRefGoogle Scholar
  5. 5.
    I. G. Szendro and J. M. López, Physical Review E, 71, No. 5, 055203 (2005).ADSCrossRefGoogle Scholar
  6. 6.
    M. Lakshmanan and D. V. Senthilkumar, Dynamics of Nonlinear Time-Delay Systems, Springer, Berlin (2011).CrossRefzbMATHGoogle Scholar
  7. 7.
    A. A. Kashchenko, J. Phys. Conf. Series, 937, No. 1, 012020 (2017).MathSciNetCrossRefGoogle Scholar
  8. 8.
    A. A. Kashchenko, Automatic Control and Computer Sciences, 51, No. 7, 639 (2017).CrossRefGoogle Scholar
  9. 9.
    A. A. Kashchenko, Automatic Control and Computer Sciences, 51, No. 7, 753 (2017).CrossRefGoogle Scholar
  10. 10.
    A. A. Kashchenko, J. Differential Equations, 266, No. 1, 562 (2019).ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    S. A. Kaschenko, Dokl. Akad. Nauk SSSR, 273, No. 2, 328 (1983).MathSciNetGoogle Scholar
  12. 12.
    S. A. Kaschenko, Dokl. Akad. Nauk SSSR, 292, No. 2, 327 (1987).MathSciNetGoogle Scholar
  13. 13.
    A. S. Dmitriev and S. A. Kaschenko, Radiotekh. Élektron., No. 12, 2381 (1981).Google Scholar
  14. 14.
    E. Grigorieva and S. Kaschenko, Regular and Chaotic Dynamics, 15, No. 2, 319 (2010).ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    D. Kaschenko, S. Kaschenko, and W. Schwarz, International J. Bifurcation and Chaos, 22, No. 8, 1250184 (2012).ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    A. N. Sharkovsky, Yu. L. Maystrenko, and E. Yu. Romanenko, Difference Equations and their Applications, Naukova Dumka, Kiev (1986).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.P. G. Demidov Yaroslavl State UniversityYaroslavlRussia

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