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

• Record Type: Journal Article
• Authors: Shaikhet, L.
• Is Part Of: Discrete dynamics in nature and society. Volume 2006(2006)
• Publication Date: 2006-06-18
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/DDNS/2006/74043
• Languages: English
• ISSNs: 1026-0226

Abstract

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.