Stability by linear approximation for time scale dynamical systems

Research output

4 Citations (Scopus)

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.
Original languageEnglish
JournalJournal of Mathematical Analysis and Applications
DOIs
Publication statusPublished - 2017

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