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 Rus. J. Nonlin. Dyn., 2020, Volume 16, Number 1, Pages 23–43 (Mi nd693)

Nonlinear physics and mechanics

Dynamics of a System of Two Simple Self-Excited Oscillators with Delayed Step-by-Step Feedback

D. S. Kashchenko, S. A. Kashchenko

P.G.Demidov Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150003 Russia

Abstract: This paper studies the dynamics of a system of two coupled self-excited oscillators of first order with on-off delayed feedback using numerical and analytical methods. Regions of “fast” and “long” synchronization are identified in the parameter space, and the problem of synchronization on an unstable cycle is examined. For small coupling coefficients it is shown by analytical methods that the dynamics of the initial system is determined by the dynamics of a special one-dimensional map.

Keywords: stability, dynamics, relaxation cycles, irregular oscillations

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 1.13560.2019/13.1 This work was carried out within the framework of the project RNOMTs (1.13560.2019/13.1) of the Ministry of Science and Higher Education.

DOI: https://doi.org/10.20537/nd200103

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MSC: 37G15, 34C23
Accepted:04.02.2020
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Citation: D. S. Kashchenko, S. A. Kashchenko, “Dynamics of a System of Two Simple Self-Excited Oscillators with Delayed Step-by-Step Feedback”, Rus. J. Nonlin. Dyn., 16:1 (2020), 23–43

Citation in format AMSBIB
\Bibitem{KasKas20} \by D. S. Kashchenko, S. A. Kashchenko \paper Dynamics of a System of Two Simple Self-Excited Oscillators with Delayed Step-by-Step Feedback \jour Rus. J. Nonlin. Dyn. \yr 2020 \vol 16 \issue 1 \pages 23--43 \mathnet{http://mi.mathnet.ru/nd693} \crossref{https://doi.org/10.20537/nd200103} \elib{https://elibrary.ru/item.asp?id=43018579} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85084470843}