On the global attractivity of systems of nonlinear difference equations (Q1855995)

The global atractivity of the positive solutions of two systems of nonlinear difference equations, \(X_{n+1}=AX_n+F(X_{n-k})\), with \(A\) an \(m\times m\) matrix and \(F\in C[[0,\infty)^m,(0,\infty)^m]\), and \(X_{n+1}=G(X_n,\dots,X_{n-k})\), \(n=0,1,\dots,\) with \(G\in C[(0,\infty)^{m(k+1)},(0,\infty)^m]\) is studied. The authors give some sufficient conditions on the spectral radius of \(A\) and in the monotony properties of the functions \(F\) and \(G\) to ensure that every positive solution of such problems is attracted to \(\overline X\), with \(\overline X\) the unique positive equilibrium of the two studied systems.