Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775252 | Journal of Mathematical Analysis and Applications | 2017 | 24 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Sergey Kryzhevich, Alexander Nazarov,