This article is cited in 1 scientific paper (total in 1 paper)
On stability of boundary equilibria in systems with cosymmetry
L. G. Kurakin
Rostov State University
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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Siberian Mathematical Journal, 2001, 42:6, 1102–1110
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
\paper On stability of boundary equilibria in systems with cosymmetry
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
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This publication is cited in the following articles:
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
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