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Regular and Chaotic Dynamics, 2024, Volume 29, Issue 1, paper published in the English version journal
DOI: https://doi.org/10.1134/S1560354724010143
(Mi rcd1255)
 

Special Issue: In Honor of Vladimir Belykh and Sergey Gonchenko Guest Editors: Alexey Kazakov, Vladimir Nekorkin, and Dmitry Turaev

Asymptotics of Self-Oscillations in Chains of Systems of Nonlinear Equations

Sergey A. Kashchenko

Regional Scientific and Educational Mathematical Center of the Yaroslavl State University, ul. Sovetskaya 14, 150003 Yaroslavl, Russia
(1)
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Abstract: We study the local dynamics of chains of coupled nonlinear systems of second- order ordinary differential equations of diffusion-difference type. The main assumption is that the number of elements of chains is large enough. This condition allows us to pass to the problem with a continuous spatial variable. Critical cases have been considered while studying the stability of the equilibrum state. It is shown that all these cases have infinite dimension. The research technique is based on the development and application of special methods for construction of normal forms. Among the main results of the paper, we include the creation of new nonlinear boundary value problems of parabolic type, whose nonlocal dynamics describes the local behavior of solutions of the original system.
Keywords: self-oscillations, dynamics, stability, coupled chains, asymptotic behavior
Funding agency Grant number
Russian Science Foundation 21-71-30011
This work was supported by the Russian Science Foundation (project no. 21-71-30011), https://rscf.ru/en/project/21-71-30011/.
Received: 29.08.2023
Accepted: 15.01.2024
Document Type: Article
MSC: 34K20
Language: English
Citation: Sergey A. Kashchenko
Citation in format AMSBIB
\Bibitem{Kas24}
\by Sergey A. Kashchenko
\mathnet{http://mi.mathnet.ru/rcd1255}
\crossref{https://doi.org/10.1134/S1560354724010143}
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