Elaydi, Saber N.; Kocic, Vlajko L. Global stability of a nonlinear Volterra difference system. (English) Zbl 0868.39003 Differ. Equ. Dyn. Syst. 2, No. 4, 337-345 (1994). Summary: We study the global asymptotic stability of the zero solution of the nonlinear Volterra difference equation \[ x(n+1)= \sum^n_{j=0} K(n,j,x(j)), \qquad n=0,1,\dots \] where \(x(0)= x_0\in \mathbb{R}^p\) is a given initial condition and where for all \(j,n= 0,1,\dots\), the function \(K(n,j,x)\) maps \(\mathbb{R}^p\) into \(\mathbb{R}^p\) and is continuous in \(x\in \mathbb{R}^p\). We consider also the linear equation \[ y(n+1)= \sum^n_{j=0} A(n,j)y(j) \] where \(y(0)= y_0\in\mathbb{R}^p\) is a given initial condition and where \(A(n,j)\) are given \(p\times p\) matrices. Cited in 7 Documents MSC: 39A11 Stability of difference equations (MSC2000) Keywords:difference system; global asymptotic stability; zero solution; nonlinear Volterra difference equation PDFBibTeX XMLCite \textit{S. N. Elaydi} and \textit{V. L. Kocic}, Differ. Equ. Dyn. Syst. 2, No. 4, 337--345 (1994; Zbl 0868.39003)