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Avtomatika i Telemekhanika, 2005, Issue 6, Pages 19–29 (Mi at1381)  
This article is cited in 3 scientific papers (total in 3 papers)

Deterministic Systems

On the conditions for invariance of the sets belonging to the phase portraits of nonlinear dynamic systems

V. P. Zhukov

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (219 kB) Citations (3)
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Abstract: Consideration was given to the conditions for invariance of the sets belonging to the phase portraits of the nonlinear dynamic systems, that is, to the conditions under which these sets consist of entire trajectories of the dynamic systems following nonlinear autonomous vector ordinary differential equations of an arbitrary order. The necessary and sufficient conditions for invariance of the phase sets as well as the sufficient conditions for nonexistence of the invariant sets were presented.
Presented by the member of Editorial Board: B. T. Polyak

Received: 20.04.2004
English version:
Automation and Remote Control, 2005, Volume 66, Issue 6, Pages 866–875
DOI: https://doi.org/10.1007/s10513-005-0130-1
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. P. Zhukov, “On the conditions for invariance of the sets belonging to the phase portraits of nonlinear dynamic systems”, Avtomat. i Telemekh., 2005, no. 6, 19–29; Autom. Remote Control, 66:6 (2005), 866–875
Citation in format AMSBIB
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\by V.~P.~Zhukov
\paper On the conditions for invariance of the sets belonging to the phase portraits of nonlinear dynamic systems
\jour Avtomat. i Telemekh.
\yr 2005
\issue 6
\pages 19--29
\mathnet{http://mi.mathnet.ru/at1381}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2157570}
\zmath{https://zbmath.org/?q=an:1113.34040}
\transl
\jour Autom. Remote Control
\yr 2005
\vol 66
\issue 6
\pages 866--875
\crossref{https://doi.org/10.1007/s10513-005-0130-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-21644440975}
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  • https://www.mathnet.ru/eng/at/y2005/i6/p19
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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