Stability by linear approximation for time scale dynamical systems

Sergey Kryzhevich; Alexander Nazarov

doi:10.1016/j.jmaa.2017.01.012

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-autonomous linear ODE theory may work for time-scale dynamics.

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Authors (2)

Sergey Kryzhevich dr hab.
- University of Texas at Dallas
Alexander Nazarov Professor
- Saint Petersburg State University

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DOI:: Digital Object Identifier (open in new tab) 10.1016/j.jmaa.2017.01.012
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Articles

Type:

artykuły w czasopismach

Published in:

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS no. 449, pages 1911 - 1934,
ISSN: 0022-247X

Language:

English

Publication year:

2017

Bibliographic description:

Kryzhevich S., Nazarov A.: Stability by linear approximation for time scale dynamical systems// JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS -, (2017), s.1911-1934

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