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Russian Mathematical Surveys, 2008, Volume 63, Issue 5, Pages 791–857
DOI: https://doi.org/10.1070/RM2008v063n05ABEH004560 (Mi rm9237) 		 
This article is cited in 69 scientific papers (total in 70 papers)

Asymptotic analysis of autoresonance models

L. A. Kalyakin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
English version PDF (2015 kB) Citations (70)
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DOI: https://doi.org/10.1070/RM2008v063n05ABEH004560
Abstract: In recent decades new problems have arisen in oscillation theory which are related to the investigation of a physical phenomenon known as autoresonance. This paper presents a survey of results on the asymptotic analysis of such problems. Systems of differential equations corresponding to non-linear non-autonomous oscillators with variable excitation frequency are considered. For their solution asymptotic formulae are constructed with respect to a small parameter or with respect to an independent variable.
Received: 10.05.2008
Russian version:
Uspekhi Matematicheskikh Nauk, 2008, Volume 63, Issue 5(383), Pages 3–72
DOI: https://doi.org/10.4213/rm9237
Bibliographic databases:
Document Type: Article
UDC: 517.956
MSC: Primary 70K30, 34C15, 34E05; Secondary 34E10, 41A60, 78M35
Language: English
Original paper language: Russian
Citation: L. A. Kalyakin, “Asymptotic analysis of autoresonance models”, Uspekhi Mat. Nauk, 63:5(383) (2008), 3–72; Russian Math. Surveys, 63:5 (2008), 791–857
Citation in format AMSBIB
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    • This publication is cited in the following 70 articles:
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    References:98
    First page:33
     
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