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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 6, Pages 1003–1013 (Mi zvmmf4576)  

This article is cited in 1 scientific paper (total in 1 paper)

On solutions to two-dimensional systems realizing the transition from an unstable equilibrium to a stable cycle

S. E. Gorodetski, A. M. Ter-Krikorov

Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

Abstract: For a two-dimensional dynamical system at $-\infty<t<+\infty$, a process describing the transition from an arbitrary neighborhood of an unstable equilibrium to a stable limit cycle is studied. The system is reduced to the Poincaré normal form. An approximate solution is constructed as a polynomial of degree $2N$ containing only even degrees of the small parameter $\varepsilon$. The functional classes to which the coefficients of this polynomial belong are described. The function space containing the exact solution differing from the approximate one by $O(\varepsilon^{2N+1})$ is determined.

Key words: dynamical system, small parameter, transition process, unstable equilibrium, stable limit cycle.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:6, 946–955

Bibliographic databases:

UDC: 519.62
Received: 20.06.2007
Revised: 10.12.2007

Citation: S. E. Gorodetski, A. M. Ter-Krikorov, “On solutions to two-dimensional systems realizing the transition from an unstable equilibrium to a stable cycle”, Zh. Vychisl. Mat. Mat. Fiz., 48:6 (2008), 1003–1013; Comput. Math. Math. Phys., 48:6 (2008), 946–955

Citation in format AMSBIB
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\by S.~E.~Gorodetski, A.~M.~Ter-Krikorov
\paper On solutions to two-dimensional systems realizing the transition from an unstable equilibrium to a~stable cycle
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2008
\vol 48
\issue 6
\pages 1003--1013
\mathnet{http://mi.mathnet.ru/zvmmf4576}
\zmath{https://zbmath.org/?q=an:1164.34429}
\transl
\jour Comput. Math. Math. Phys.
\yr 2008
\vol 48
\issue 6
\pages 946--955
\crossref{https://doi.org/10.1134/S0965542508060079}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. E. Gorodetski, A. M. Ter-Krikorov, “On solutions of three-dimensional systems describing the transition from an unstable equilibrium to a stable cycle”, Comput. Math. Math. Phys., 51:4 (2011), 575–585  mathnet  crossref  mathscinet  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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