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Stability by linear approximation for time scale dynamical systemsSergey Kryzhevich,
Alexander Nazarov, 2017, original scientific article
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
Published in RUNG: 15.03.2017; Views: 4953; Downloads: 161
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