On the behavior of positive solutions of the system of rational difference equations xn+1 = xn-1/(ynxn-1+1), yn+1 = yn-1/(xnyn-1+1)

In this paper, we investigate the positive solutions of the system of difference equations x"n"+"1=x"n"-"1y"nx"n"-"1+1,y"n"+"1=y"n"-"1x"ny"n"-"1+1, where y"0,y"-"1,x"0,x"-"[email protected]?[0,+~).

[1]  B. Demir,et al.  On the Solutions of the System of Difference Equations xn+1=max{A/xn,yn/xn}, yn+1=max{A/yn,xn/yn} , 2009 .

[2]  Cengiz Çinar,et al.  On the solutions of the difference equation xn+1 = xn-1/-1+axnxn-1 , 2004, Appl. Math. Comput..

[3]  Z. Nurkanović,et al.  Global behavior of a three-dimensional linear fractional system of difference equations , 2005 .

[4]  C. J. Schinas,et al.  On the system of two difference equations xn+1=∑i=0kAi/yn−ipi, yn+1=∑i=0kBi/xn−iqi , 2002 .

[5]  Yu Zhang,et al.  On the nonlinear difference equation system xn+1=A+yn-m/xn, yn+1=A+xn-m/yn , 2007, Comput. Math. Appl..

[6]  C. J. Schinas,et al.  On a System of Two Nonlinear Difference Equations , 1998 .

[7]  Cengiz Çinar,et al.  On the difference equation xn+1 = xn-1 / (-1+xnxn-1) , 2004, Appl. Math. Comput..

[8]  I. Yalçinkaya On the Global Asymptotic Stability of a Second-Order System of Difference Equations , 2008 .

[9]  Mustafa R. S. Kulenovic,et al.  A coupled system of rational difference equations , 2002 .

[10]  Cengiz Çinar,et al.  On the positive solutions of the difference equation system xn+1 = 1/yn, yn+1 = yn/xn-1yn-1 , 2004, Appl. Math. Comput..

[11]  James F. Selgrade,et al.  Global asymptotic behavior of a two-dimensional difference equation modelling competition , 2003 .

[12]  David J. Evans,et al.  On the system of rational difference equations xn=A + 1/yn-p, yn=A+yn-1/xn-tyn-s , 2006, Appl. Math. Comput..

[13]  Xiaofan Yang,et al.  On the system of rational difference equations xn=A+yn−1/xn−pyn−q,yn=A+xn−1/xn−ryn−s , 2005 .

[14]  I. Yalçinkaya,et al.  On the Solutions of Systems of Difference Equations , 2008 .

[15]  A. Y. Özban On the positive solutions of the system of rational difference equations xn+1=1/yn−k, yn+1=yn/xn−myn−m−k , 2006 .

[16]  Sen Bai,et al.  On the system of high order rational difference equations xn=a/yn-p, yn=byn-p/(xn-qyn-q) , 2005, Appl. Math. Comput..

[17]  Ahmet Yaşar Özban,et al.  On the system of rational difference equations xn=a/yn-3, yn=byn-3/xn-qyn-q , 2007, Appl. Math. Comput..

[18]  Garyfalos Papaschinopoulos,et al.  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 , 2004, Appl. Math. Lett..

[19]  I. Yalçinkaya,et al.  Global asymptotic stability of a system of difference equations , 2008 .