Conditional Stability and Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R2 - Josef Diblík; Hana Halfarová; Jan Šafařík (Discrete Dynamics in Nature and Society)
Two-dimensional linear discrete systems x(k+1)=Ax(k)+∑l=1nBlxl(k-ml),  k≥0, are analyzed, where m1,m2,…,mn are constant integer delays, 0<m1<m2<⋯<mn, A, B1,…,Bn are constant 2×2 matrices, A=(aij), Bl=(bijl),  i,j=1,2,  l=1,2,…,n, and x:{-mn,-mn+1,…}→R2. Under the assumption that the system is weakly delayed, the asymptotic behavior of its solutions is studied and asymptotic formulas are derived.