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 Sibirsk. Mat. Zh., 2001, Volume 42, Number 6, Pages 1324–1334 (Mi smj1389)

On stability of boundary equilibria in systems with cosymmetry

L. G. Kurakin

Rostov State University

Abstract: Using the direct Lyapunov method, we study the stability of an equilibrium of a cosymmetric vector field in the case when the stability spectrum lies in the closure of the left half-plane and the neutral spectrum (lying on the imaginary axis) consists of simple eigenvalues zero and a pair of purely imaginary numbers. Owing to cosymmetry, this equilibrium state is a member of a continuous one-parameter family of equilibria with a variable stability spectrum. We use theorems on asymptotic stability with respect to part of variables. We find stability criteria in the case of general position, as well for all degenerations of codimension one and one case of codimension two. As a result, we give description for dangerous and safe stability boundaries.

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English version:
Siberian Mathematical Journal, 2001, 42:6, 1102–1110

Bibliographic databases:

UDC: 517.958

Citation: L. G. Kurakin, “On stability of boundary equilibria in systems with cosymmetry”, Sibirsk. Mat. Zh., 42:6 (2001), 1324–1334; Siberian Math. J., 42:6 (2001), 1102–1110

Citation in format AMSBIB
\Bibitem{Kur01} \by L.~G.~Kurakin \paper On stability of boundary equilibria in systems with cosymmetry \jour Sibirsk. Mat. Zh. \yr 2001 \vol 42 \issue 6 \pages 1324--1334 \mathnet{http://mi.mathnet.ru/smj1389} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1876818} \transl \jour Siberian Math. J. \yr 2001 \vol 42 \issue 6 \pages 1102--1110 \crossref{https://doi.org/10.1023/A:1012844610886} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000172981200008} 

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• http://mi.mathnet.ru/eng/smj/v42/i6/p1324

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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. L. G. Kurakin, V. I. Yudovich, “On equilibrium bifurcations in the cosymmetry collapse of a dynamical system”, Siberian Math. J., 45:2 (2004), 294–310