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Stability by linear approximation for time scale dynamical systems. / Kryzhevich, Sergey; Nazarov, Alexander.

в: Journal of Mathematical Analysis and Applications, Том 449, № 2, 2017, стр. 1911-1934.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Kryzhevich, S & Nazarov, A 2017, 'Stability by linear approximation for time scale dynamical systems', Journal of Mathematical Analysis and Applications, Том. 449, № 2, стр. 1911-1934. https://doi.org/10.1016/j.jmaa.2017.01.012

APA

Kryzhevich, S., & Nazarov, A. (2017). Stability by linear approximation for time scale dynamical systems. Journal of Mathematical Analysis and Applications, 449(2), 1911-1934. https://doi.org/10.1016/j.jmaa.2017.01.012

Vancouver

Kryzhevich S, Nazarov A. Stability by linear approximation for time scale dynamical systems. Journal of Mathematical Analysis and Applications. 2017;449(2):1911-1934. https://doi.org/10.1016/j.jmaa.2017.01.012

Author

Kryzhevich, Sergey ; Nazarov, Alexander. / Stability by linear approximation for time scale dynamical systems. в: Journal of Mathematical Analysis and Applications. 2017 ; Том 449, № 2. стр. 1911-1934.

BibTeX

@article{32ec536c515445b0a18bdaaeadffa308,
title = "Stability by linear approximation for time scale dynamical systems",
abstract = "We study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents (a common tool of the theory of linear ODEs) to study stability of solutions. Also, time scale versions of the famous Chetaev's theorem on conditional instability are proved. In a nutshell, we have developed a completely new technique in order to demonstrate that methods of non-authonomous linear ODE theory may work for time-scale dynamics.",
keywords = "time scale system, linearization, Lyapunov functions, Millionschikov rotations, stability",
author = "Sergey Kryzhevich and Alexander Nazarov",
year = "2017",
doi = "10.1016/j.jmaa.2017.01.012",
language = "English",
volume = "449",
pages = "1911--1934",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Elsevier",
number = "2",

}

RIS

TY - JOUR

T1 - Stability by linear approximation for time scale dynamical systems

AU - Kryzhevich, Sergey

AU - Nazarov, Alexander

PY - 2017

Y1 - 2017

N2 - We study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents (a common tool of the theory of linear ODEs) to study stability of solutions. Also, time scale versions of the famous Chetaev's theorem on conditional instability are proved. In a nutshell, we have developed a completely new technique in order to demonstrate that methods of non-authonomous linear ODE theory may work for time-scale dynamics.

AB - We study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents (a common tool of the theory of linear ODEs) to study stability of solutions. Also, time scale versions of the famous Chetaev's theorem on conditional instability are proved. In a nutshell, we have developed a completely new technique in order to demonstrate that methods of non-authonomous linear ODE theory may work for time-scale dynamics.

KW - time scale system

KW - linearization

KW - Lyapunov functions

KW - Millionschikov rotations

KW - stability

U2 - 10.1016/j.jmaa.2017.01.012

DO - 10.1016/j.jmaa.2017.01.012

M3 - Article

VL - 449

SP - 1911

EP - 1934

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -

ID: 7733750