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

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)[[PQ_REPLACE:[math]] ], xi(n+1)=(ai-1xi-1(n)+b i-1)/xi-2 (n-1), i =3,4,...,k, where ai[[PQ_REPLACE:[m ath]]], bi[[PQ_REPLACE:[m ath]]], i =1,2,...,k, are positive c...

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Bibliographic Details
Published in:Advances in difference equations 2007-01, Vol.2007, p.1-14
Main Authors: Papaschinopoulos, G., Schinas, C. J., Stefanidou, G.
Format: Article
Language:English
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Summary: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)[[PQ_REPLACE:[math]] ], xi(n+1)=(ai-1xi-1(n)+b i-1)/xi-2 (n-1), i =3,4,...,k, where ai[[PQ_REPLACE:[m ath]]], bi[[PQ_REPLACE:[m ath]]], i =1,2,...,k, are positive constants, k > =3[[PQ_REPLAC E:[math]]] 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.
ISSN:1687-1839
1687-1847
DOI:10.1155/2007/31272