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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 $A>0$.

39A11Stability of difference equations (MSC2000)
Full Text: DOI
[1] Kocic, V. L.; Ladas, G.: Global behavior of nonlinear difference equations of higher order with applications. (1993) · Zbl 0787.39001
[2] Camouzis, E.; Papaschinopoulos, G.: Global asymptotic behavior of positive solutions on the system of rational difference equations xn+1=1+xn/yn-m,yn+1=1+yn/xn-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 xn+1=A+xn/xn-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 xn+1=A+xn-1/yn, yn+1=A+yn-1/xn. 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 xn=A+yn-1xn-pyn-q, yn=A+xn-1xn-ryn-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 $xn+1={\alpha}+$xn-kxn. Applied mathematics and computation 147, 163-167 (2004) · Zbl 1042.39001