Abstract:
The dynamics of second-order equations with nonlinear delayed feedback and a large coefficient of a delayed equation is investigated using asymptotic methods. Based on special methods of quasi-normal forms, a new construction is elaborated for obtaining the main terms of asymptotic expansions of asymptotic residual solutions. It is shown that the dynamical properties of the above equations are determined mostly by the behavior of the solutions of some special families of parabolic boundary value problems. A comparative analysis of the dynamics of equations with the delayed feedback of three types is carried out.
Keywords:
delay, feedback, nonlinear dynamics, boundary value problems.
Citation:
Sergey A. Kashchenko, “The Dynamics of Second-order Equations with Delayed Feedback and a Large Coefficient of Delayed Control”, Regul. Chaotic Dyn., 21:7-8 (2016), 811–820
\Bibitem{Kas16}
\by Sergey A. Kashchenko
\paper The Dynamics of Second-order Equations with Delayed Feedback and a Large Coefficient of Delayed Control
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 7-8
\pages 811--820
\mathnet{http://mi.mathnet.ru/rcd227}
\crossref{https://doi.org/10.1134/S1560354716070042}
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Linking options:
https://www.mathnet.ru/eng/rcd227
https://www.mathnet.ru/eng/rcd/v21/i7/p811
This publication is cited in the following 3 articles:
S. A. Kaschenko, A. O. Tolbei, “Kvazinormalnye formy dlya sistem dvukh uravnenii s bolshim zapazdyvaniem”, Izvestiya vuzov. PND, 32:6 (2024), 782–795
S. A. Kaschenko, A. O. Tolbey, “Dynamics of a system of two equations with a large delay”, Dokl. Math., 108:2 (2023), 369–373
Sergey Kashchenko, “Van der Pol Equation with a Large Feedback Delay”, Mathematics, 11:6 (2023), 1301
Citation in format AMSBIB
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