On some \(k\)-dimensional cyclic systems of difference equations (Q1957585)

Summary: Motivated by \textit{B. D. Iričanin} and \textit{S. Stević}'s paper [Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 13, No.~3--4, 499--507 (2006; Zbl 1098.39003)] in which for the first time some cyclic systems of difference equations were considered, we study here the global attractivity of some nonlinear \(k\)-dimensional cyclic systems of higher-order difference equations. To do this, we use the transformation method from [\textit{K. S. Berenhaut} et al., Appl. Math. Lett. 20, No.~1, 54--58 (2007; Zbl 1131.39006); and \textit{K. S. Berenhaut} and \textit{S. Stević}, J. Math. Anal. Appl. 326, No.~2, 940--944 (2007; Zbl 1112.39002)]. The main results in this paper also extend our recent results in the work of [\textit{W. Liu} and \textit{X. Yang}, The global behavior of two higher-order symmetric recursive equations (2010) in press).