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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 12, Pages 12–18 (Mi ivm9181)  

This article is cited in 2 scientific papers (total in 2 papers)

On a method of evaluation of attraction domain for fixed point of nonlinear point mapping of arbitrary dimension

O. G. Antonovskayaa, V. I. Goryunovb

a University of Architecture and Civil Engineering, 65 Alekseevskaya str., Nizhny Novgorod, 603950 Russia
b Nizhny Novgorod State University, 23 Gagarin Ave., Nizhny Novgorod, 603950 Russia

Abstract: In this paper we describe the method of attraction domain evaluation for equilibrium states of nonlinear discrete dynamic system based on Lyapunov functions method. Attraction domain evaluation size is equilibrium state neighborhood where the first difference of Lyapunov function is negative. Lyapunov function is chosen as positive quadratic form for which the negativity of its first difference by virtue of linearized system is guaranteed with given supply. We propose the method of attraction domain extension.

Keywords: discrete dynamic system, macro-structure of state space, Lyapunov function method.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:12, 9–14

Bibliographic databases:

UDC: 517.968
Received: 06.05.2015

Citation: O. G. Antonovskaya, V. I. Goryunov, “On a method of evaluation of attraction domain for fixed point of nonlinear point mapping of arbitrary dimension”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 12, 12–18; Russian Math. (Iz. VUZ), 60:12 (2016), 9–14

Citation in format AMSBIB
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\paper On a~method of evaluation of attraction domain for fixed point of nonlinear point mapping of arbitrary dimension
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 12
\pages 12--18
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\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 12
\pages 9--14
\crossref{https://doi.org/10.3103/S1066369X16120021}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. G. Antonovskaya, “Primenenie kvadratichnykh funktsii Lyapunova pri reshenii prikladnykh dinamicheskikh zadach”, Mezhdunar. nauch.-issled. zhurn., 2017, no. 8-2(62), 142–147  mathnet  crossref
    2. O. G. Antonovskaya, “Primenenie kvadratichnykh funktsii Lyapunova k zadacham ustoichivosti sistem s zapazdyvaniem”, Izv. vuzov. Matem., 2019, no. 10, 15–20  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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