Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 74043, 16 pages

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

L. Shaikhet

Department of Higher Mathematics, Donetsk State University of Management, Chelyuskintsev street 163-A, Donetsk 83015, Ukraine

Received 20 January 2006; Accepted 24 March 2006

Copyright © 2006 L. Shaikhet. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.