## On the nonlinear difference equation system $$x_{n+1}=A+y_{n - m}/x_n,y_{n+1}=A+x_{n - m}/y_n$$.(English)Zbl 1152.39312

Summary: We study the boundedness, persistence, and global asymptotic stability of positive solutions of the system of two difference equations $X_{n+1}=A+\frac{y_{n-m}}{x_n},\qquad y_{n+1}=A+\frac{x_{n-m}}{y_n},\quad n=0,1,\dots$ where $$A>0$$.

### MSC:

 39A11 Stability of difference equations (MSC2000)
Full Text:

### References:

 [1] Kocic, V.L.; Ladas, G., Global behavior of nonlinear difference equations of higher order with applications, (1993), Kluwer Academic Dordrecht · Zbl 0787.39001 [2] Camouzis, E.; Papaschinopoulos, G., Global asymptotic behavior of positive solutions on the system of rational difference equations $$x_{n + 1} = 1 + x_n / y_{n - m}, y_{n + 1} = 1 + y_n / x_{n - m}$$, Applied mathematics letters, 17, 733-737, (2004) · Zbl 1064.39004 [3] Clark, D.; Kulenović, M.R.S., A coupled system of rational difference equations, Computers and mathematics with applications, 43, 849-867, (2002) · Zbl 1001.39017 [4] Clark, D.; Kulenović, M.R.S.; Selgrade, J.F., Global asymptotic behavior of a two-dimensional difference equation modelling competition, Nonlinear analysis, 52, 1765-1776, (2003) · Zbl 1019.39006 [5] Papaschinopoulos, G.; Papadopoulos, B.K., On the fuzzy difference equation $$x_{n + 1} = A + x_n / x_{n - m}$$, Fuzzy sets and systems, 129, 73-81, (2002) · Zbl 1016.39015 [6] Papaschinopoulos, G.; Schinas, C.J., On the system of two nonlinear difference equations $$x_{n + 1} = A + x_{n - 1} / y_n$$, $$y_{n + 1} = A + y_{n - 1} / x_n$$, International journal of mathematics & mathematical sciences, 12, 839-848, (2000) · Zbl 0960.39003 [7] Schinas, C.J., Invariants for difference equations and systems of difference equations of rational form, Journal of mathematical analysis and applications, 216, 164-179, (1997) · Zbl 0889.39006 [8] Yang, X.F., On the system of rational difference equations $$x_n = A + \frac{y_{n - 1}}{x_{n - p} y_{n - q}}$$, $$y_n = A + \frac{x_{n - 1}}{x_{n - r} y_{n - s}}$$, Journal of mathematical analysis and applications, 307, 305-311, (2005) [9] El-Owaidy, H.M.; Ahmed, A.M.; Mousa, M.S., On asymptotic behaviour of the difference equation $$x_{n + 1} = \alpha + \frac{x_{n - k}}{x_n}$$, Applied mathematics and computation, 147, 163-167, (2004) · Zbl 1042.39001
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.