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Model. Anal. Inform. Sist., 2017, Volume 24, Number 5, Pages 649–654 (Mi mais589)  

A family of non-rough cycles in a system of two coupled delayed generators

A. A. Kashchenko

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

Abstract: In this paper, we consider the nonlocal dynamics of the model of two coupled oscillators with delayed feedback. This model has the form of a system of two differential equations with delay. The feedback function is non-linear, finite and smooth. The main assumption in the problem is that the coupling between the generators is sufficiently small. With the help of asymptotic methods we investigate the existence of relaxation periodic solutions of a given system. For this purpose, a special set is constructed in the phase space of the original system. Then we build an asymptotics of the solutions of the given system with initial conditions from this set. Using this asymptotics, a special mapping is constructed. Dynamics of this map describes the dynamics of the original problem in general. It is proved that all solutions of this mapping are non-rough cycles of period two. As a result, we formulate conditions for the coupling parameter such that the initial system has a two-parameter family of non-rough inhomogeneous relaxation periodic asymptotic (with respect to the residual) solutions.

Keywords: large parameter, relaxation oscillation, periodic solution, asymptotics, delay.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.6074.2017/П220
This work was supported by State assignment, work No 1.6074.2017/Π220.


DOI: https://doi.org/10.18255/1818-1015-2017-5-649-654

Full text: PDF file (492 kB)
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UDC: 517.9
Received: 15.06.2017

Citation: A. A. Kashchenko, “A family of non-rough cycles in a system of two coupled delayed generators”, Model. Anal. Inform. Sist., 24:5 (2017), 649–654

Citation in format AMSBIB
\Bibitem{Kas17}
\by A.~A.~Kashchenko
\paper A family of non-rough cycles in a system of two coupled delayed generators
\jour Model. Anal. Inform. Sist.
\yr 2017
\vol 24
\issue 5
\pages 649--654
\mathnet{http://mi.mathnet.ru/mais589}
\crossref{https://doi.org/10.18255/1818-1015-2017-5-649-654}
\elib{http://elibrary.ru/item.asp?id=30353173}


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