A new view on one problem of asymptotic behavior of solutions of delay difference equations

Abstract

One known theorem on the asymptotic behavior of solution of linear delay difference equation is considered where a stability criterion is derived via a positive root of the corresponding characteristic equation. Two new directions for further investigation are proposed. The first direction is connected with a weakening of the known stability criterion; the second one is connected with consideration of negative and complex roots of the characteristic equation. A lot of pictures with stability regions and trajectories of considered processes are presented for visual demonstration of the proposed directions.