A new view on one problem of asymptotic behavior of solutions of delay difference equations. (18th June 2006) - Shaikhet, L.
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.