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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 12, Pages 2141–2150 (Mi zvmmf69)  
This article is cited in 43 scientific papers (total in 43 papers)

Local dynamics of equations with large delay

I. S. Kashchenko

Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia
Full-text PDF (1173 kB) Citations (43)
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Abstract: The local dynamics of a differential equation with large delay is analyzed using the normal forms technique. It is shown that, in the critical cases, families of parabolic equations play the role of infinite-dimensional normal forms. It is demonstrated analytically that even a very simple first-order delay equation can have a complicated dynamical behavior. Methods for constructing classes of stable modes for such equations are described. The proposed methods are extended for the case of secondorder equations.
Key words: dynamics of ordinary differential equations with large delay, normal forms technique, parabolic equations, roots of quasi-polynomials.
Received: 03.12.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 12, Pages 2172–2181
DOI: https://doi.org/10.1134/S0965542508120075
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: I. S. Kashchenko, “Local dynamics of equations with large delay”, Zh. Vychisl. Mat. Mat. Fiz., 48:12 (2008), 2141–2150; Comput. Math. Math. Phys., 48:12 (2008), 2172–2181
Citation in format AMSBIB
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    • This publication is cited in the following 43 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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