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

Abstract

We consider the following system of Lyness-type difference equations: x1(n+1)=(akxk(n)+bk)/xk−1(n−1), x2(n+1)=(a1x1(n)+b1)/xk(n−1), xi(n+1)=(ai−1xi−1(n)+bi−1)/xi−2(n−1), i=3,4,…,k, where ai, bi, i=1,2,…,k, are positive constants, k≥3 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.