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Title:Stability by linear approximation for time scale dynamical systems
Authors:ID Kryzhevich, Sergey, University of Nova Gorica (Author)
ID Nazarov, Alexander, Saint-Petersburg State University (Author)
Files:URL http://www.sciencedirect.com/science/article/pii/S0022247X17300343
 
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:UNG - University of Nova Gorica
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.
Keywords:Time scale system, Linearization, Lyapunov functions, Millionschikov rotations, Stability
Year of publishing:2017
Number of pages:1911-1934
Numbering:2, 449
PID:20.500.12556/RUNG-3021-6f6047f3-9a52-fdef-e71a-cbfbcaee9576 New window
COBISS.SI-ID:4718075 New window
DOI:http://dx.doi.org/10.1016/j.jmaa.2017.01.012 New window
NUK URN:URN:SI:UNG:REP:RZ6ITMLK
Publication date in RUNG:15.03.2017
Views:3953
Downloads:160
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Record is a part of a journal

Title:Journal of Mathematical Analysis and Applications
Publisher:Elsevier
Year of publishing:2017
ISSN:0022-247X

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Licensing start date:15.03.2017

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