Sun, Taixiang; Fan, Xiyu; Han, Caihong; Qin, Bin Global asymptotic stability of the nonlinear difference equation \(x_{n+1}=f(x_n,x_{n-k})\). (English) Zbl 1141.39305 J. Guangxi Univ., Nat. Sci. 32, No. 2, 93-97 (2007). Summary: A nonlinear difference equation \(x_{n+1}=f(x_n, x_{n-k}),\) \(n=0, 1,\dots\), where \(x_{-k}, x_{-k+1}, \dots, x_0 \in (0, +\infty)\) is considered. The sufficient conditions are obtained under which the unique positive equilibrium of this equation is globally asymptotically stable. MSC: 39A11 Stability of difference equations (MSC2000) 39A10 Additive difference equations Keywords:global asymptotic stability; nonlinear difference equation; positive equilibrium PDFBibTeX XMLCite \textit{T. Sun} et al., J. Guangxi Univ., Nat. Sci. 32, No. 2, 93--97 (2007; Zbl 1141.39305)