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Ufa Mathematical Journal, 2016, Volume 8, Issue 3, Pages 58–78
DOI: https://doi.org/10.13108/2016-8-3-58 (Mi ufa325) 		 
This article is cited in 6 scientific papers (total in 6 papers)

The asymptotic formulae in the problem on constructing hyperbolicity and stability regions of dynamical systems

L. S. Ibragimovaa, I. Zh. Mustafinab, M. G. Yumagulovb

a Bashkir State Agricultural University, Ufa
b Bashkir State University, Ufa
English version PDF (503 kB) Citations (6)
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DOI: https://doi.org/10.13108/2016-8-3-58
Abstract: The paper proposes a new general method allowing one to study the problem on constructing hyperbolicity and stability regions for nonlinear dynamical systems. The method is based on a modification of M. Rozo method for studying the stability of linear systems with periodic coefficients depending on a small parameter and on the asymptotic formulae in the perturbation theory of linear operators. We obtain approximate formulae describing the boundary of hyperbolicity and stability regions. As an example, we provide the scheme for constructing the stability regions for Mathieu equation.
Keywords: hyperbolicity regions, stability regions, dynamical systems, small parameter, asymptotic formula.
Received: 24.03.2016
Russian version:
Ufimskii Matematicheskii Zhurnal, 2016, Volume 8, Issue 3, Pages 59–81
Bibliographic databases:
Document Type: Article
UDC: 517.91
MSC: 34D20,37C60
Language: English
Original paper language: Russian
Citation: L. S. Ibragimova, I. Zh. Mustafina, M. G. Yumagulov, “The asymptotic formulae in the problem on constructing hyperbolicity and stability regions of dynamical systems”, Ufimsk. Mat. Zh., 8:3 (2016), 59–81; Ufa Math. J., 8:3 (2016), 58–78
Citation in format AMSBIB
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\pages 59--81
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\transl
\jour Ufa Math. J.
\yr 2016
\vol 8
\issue 3
\pages 58--78
\crossref{https://doi.org/10.13108/2016-8-3-58}
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  • https://doi.org/10.13108/2016-8-3-58
  • https://www.mathnet.ru/eng/ufa/v8/i3/p59
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Уфимский математический журнал
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    Abstract page:301
    Russian version PDF:119
    English version PDF:12
    References:42
     
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