Matsunaga, Hideaki A note on asymptotic stability of delay difference systems. (English) Zbl 1082.39007 J. Inequal. Appl. 2005, No. 2, 119-125 (2005). The paper deals with linear delay difference system \(x_{n+1} - x_n = A x_{n-k}, n=0,1,\dots,\) where \(A\) is a \(2 \times 2\) real matrix and \(k\) is a nonnegative integer. The author gives explicit necessary and sufficient conditions for the asymptotic stability of the system in the term of the determinant of \(A\), the trace of \(A\) and the delay \(k.\) As an application, the local asymptotic stability of the positive equilibrium of the Lotka-Volterra difference system are investigated. Reviewer: Victor I. Tkachenko (Kyïv) Cited in 5 Documents MSC: 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis 34K20 Stability theory of functional-differential equations Keywords:linear delay difference system; asymptotic stability; positive equilibrium; Lotka-Volterra difference system PDFBibTeX XMLCite \textit{H. Matsunaga}, J. Inequal. Appl. 2005, No. 2, 119--125 (2005; Zbl 1082.39007) Full Text: DOI EuDML