Advances in Difference Equations
Volume 2007 (2007), Article ID 31272, 13 pages
doi:10.1155/2007/31272

On a k-Order System of Lyness-Type Difference Equations

G. Papaschinopoulos , C.J. Schinas and G. Stefanidou

School of Engineering, Democritus University of Thrace, Xanthi 67100, Greece

Abstract

We consider the following system of Lyness-type difference equations: x1(n+1)=(akxk(n)+bk)/xk1(n1), x2(n+1)=(a1x1(n)+b1)/xk(n1), xi(n+1)=(ai1xi1(n)+bi1)/xi2(n1), i=3,4,,k, where ai, bi, i=1,2,,k, are positive constants, k3 is an integer, and the initial values are positive real numbers. We study the existence of invariants, the boundedness, the persistence, and the periodicity of the positive solutions of this system.