Linear difference equations and exponential polynomials

Linear Difference Equations

Dynamic economic models are a useful tool to study economic dynamics and get a better understanding of relevant phenomena such as growth and business cycle. Equilibrium conditions are normally identified by a system of difference equations and a set of boundary conditions (describing limit values of some variables). Thus, studying equilibrium properties requires studying the properties of a sys...

Linear difference and differential equations

On Exponential Dichotomy 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...

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.