Instability of Discrete Systems
MetadataShow full metadata
In this paper, we give criteria for instability and asymptotic instability for the null solution to the non-autonomous system of difference equations y(t + 1) = A(t)y(t) + f(t,y(t)), f(t,0) = 0, when the system x(t + 1) = (t)x(t) is unstable. In particular for A constant, we study instability from a new point of view. Our results are obtained using the method of discrete dichotomies, and cover a class of difference systems for which instability properties cannot be deduced from the classical results by Perron and Coppel.