Discrete Dynamics in Nature and Society
Volume 3 (1999), Issue 1, Pages 57-63
doi:10.1155/S1026022699000084
Abstract
Let Cn be the set of n complex vectors endowed with a norm ‖⋅‖Cn. Let A,B be two complex n×n matrices and τ a positive integer. In the present paper we consider the nonlinear difference equation with delay of the type uk+1=Auk+Buk−τ+Fk(uk,uk−τ), k=0,1,2,…, where Fk:Cn×Cn→Cn satisfies the condition ‖Fk(x,y)‖Cn≤p‖x‖Cn+q‖y‖Cn, k=0,1,2,…, where p and q are positive constants. In this paper, absolute stability conditions for this equation are established.