×

zbMATH — the first resource for mathematics

Global asymptotic behavior of positive solutions on the system of rational difference equations \(x_{n+1}=1+x_ n/y_{n-m}, y_ {n+1}=1+y_ n/x_{n-m}\). (English) Zbl 1064.39004
It is shown that every positive solution of the system in the title with \(m\in\mathbb{N}\) converges to an equilibrium \((x,y)\) with \(x> 1\) and \(y= x/(x- 1)\).

MSC:
39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Papaschinopoulos, G; Papadopoulos, B.K, On the fuzzy difference equation \(xn+1 = A + xnxn−m\), Fuzzy sets and systems, 129, 73-81, (2002) · Zbl 1016.39015
[2] Abu-Saris, R.M; DeVault, R, Global stability of \(yn+1 = A + ynyn−k\), Appl. math. lett., 16, 2, 173-178, (2003) · Zbl 1049.39002
[3] DeVault, R; Ladas, G; Schultz, S.W, On the recursive sequence \(xn+1 = Axn + 1xn−2\), (), 3257-3261, (11) · Zbl 0904.39012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.