On the exponential stability of two-dimensional nonautonomous difference systems which have a weighted homogeneity of the solution

Abstract

The present paper is considered a two-dimensional difference system: (Formula Presented) where all coefficients are real-valued sequences; p and p* are positive numbers satisfying (Formula Presented). The aim of this paper is to clarify that uniform asymptotic stability and exponential stability are equivalent for the above system. To illustrate the obtained results, an example is given. In addition, a figure of a solution orbit which is drawn by a computer is also attached for a deeper understanding.