New criteria for exponential stability of variational difference equations

On Exponential Stability of Variational Difference Equations

We prove that a general system of variational difference equations is uniformly exponentially stable if and only if certain associated sets are of the second category. We also deduce necessary and sufficient conditions for uniform exponential stability of systems with uniformly bounded coefficients. We apply our results for the study of exponential stability of linear skew-product flows, genera...

On Exponential Dichotomy of Variational Difference Equations

Exponential Stability in Nonlinear Difference Equations

Non-negative definite Lyapunov functionals are employed to obtain sufficient conditions that guarantee exponential stability of the zero solution of a nonlinear discrete system. The theory is illustrated with several examples.

On Exponential Stability of Variational Nonautonomous Difference Equations in Banach Spaces∗

In this paper we study two concepts of exponential stability for variational nonautonomous difference equations in Banach spaces. Characterizations of these concepts are given. The obtained results can be considered as generalizations for variational nonautonomous difference equations of some well-known theorems due to Barbashin and Datko . MSC: 34D05, 34D20, 93D20 keywords: variational differe...

On the Stability of Some Systems of Exponential Difference Equations

In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, w...