Geodesic
Semi-Invariant Form of Equilibrium Stability Criteria for Systems with One Cosymmetry
Russian journal of nonlinear dynamics, Tome 15 (2019) no. 4, pp. 525-531.

Voir la notice de l'article provenant de la source Math-Net.Ru

The systems of differential equations with one cosymmetry are considered [1]. The ordinary object for such systems is a one-dimensional continuous family of equilibria. The stability spectrum changes along this family, but it necessarily contains zero. We consider the nondegeneracy condition, thus the boundary equilibria separate the family on linearly stable and instable areas. The stability of the boundary equilibria depends on nonlinear terms of the system. The stability problem for the systems with one cosymmetry is studied in [2]. The general problem is to apply the stability criteria one needs to compute coefficients of the model system. It is especially difficult if the system has a large dimension, while a number of critical variables may be small. A method for calculating coefficients is proposed in [3]. In this work the expressions for the known stability criteria are proposed in a form convenient for calculation. The explicit formulas of the coefficients of the model system are given in semi-invariant form. They are expressed using the generalized eigenvectors of the linear matrix and its conjugate matrix.
Keywords: stability, critical case, neutral manifold, cosymmetry
Mots-clés : semi-invariant form. 
@article{ND_2019_15_4_a11,
     author = {L. G. Kurakin and A. V. Kurdoglyan},
     title = {Semi-Invariant {Form} of {Equilibrium} {Stability} {Criteria} for {Systems} with {One} {Cosymmetry}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {525--531},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2019_15_4_a11/}
}
TY  - JOUR
AU  - L. G. Kurakin
AU  - A. V. Kurdoglyan
TI  - Semi-Invariant Form of Equilibrium Stability Criteria for Systems with One Cosymmetry
JO  - Russian journal of nonlinear dynamics
PY  - 2019
SP  - 525
EP  - 531
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2019_15_4_a11/
LA  - en
ID  - ND_2019_15_4_a11
ER  - 
%0 Journal Article
%A L. G. Kurakin
%A A. V. Kurdoglyan
%T Semi-Invariant Form of Equilibrium Stability Criteria for Systems with One Cosymmetry
%J Russian journal of nonlinear dynamics
%D 2019
%P 525-531
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2019_15_4_a11/
%G en
%F ND_2019_15_4_a11
L. G. Kurakin; A. V. Kurdoglyan. Semi-Invariant Form of Equilibrium Stability Criteria for Systems with One Cosymmetry. Russian journal of nonlinear dynamics, Tome 15 (2019) no. 4, pp. 525-531. http://geodesic.mathdoc.fr/item/ND_2019_15_4_a11/

[1] Mat. Zametki, 49:5 (1991), 142–148 (Russian) | DOI | MR | Zbl

[2] Mat. Zametki, 63:4 (1998), 572–578 (Russian) | DOI | DOI | MR | Zbl

[3] Prikl. Mat. Mekh., 50:5 (1986), 707–711 (Russian) | DOI | MR | Zbl

[4] Pliss, V. A., “A Reduction Principle in the Theory of Stability of Motion”, Izv. Akad. Nauk SSSR Ser. Mat., 28:6 (1964), 1297–1324 (Russian) | MR | Zbl

[5] Arnold, V. I., Additional Chapters of the Theory of Differential Equations, Nauka, Moscow, 1978, 304 pp. (Russian) | MR

[6] Rumyantsev, V. V. and Oziraner, A. S., Motion Stability and Stabilization with Respect to Part of Variables, Nauka, Moscow, 1987, 256 pp. (Russian) | MR | Zbl