On a system of difference equations

Abstract We show that the system of difference equations x n + 1 = ax n - 1 by n x n - 1 + c , y n + 1 = α y n - 1 β x n y n - 1 + γ , n ∈ N 0 , where the parameters a , b , c , α , β , γ and initial values x −1 , x 0 , y −1 , y 0 are real numbers, can be solved, considerably improving the results in the literature.

[1]  Stevo Stevic.  Global stability of some symmetric difference equations , 2010, Appl. Math. Comput..

[2]  Stevo Stevic,et al.  The global attractivity of the rational difference equation yn = (yn-k + yn-m) / (1 + yn-k yn-m) , 2007, Appl. Math. Lett..

[3]  Stevo Stevic,et al.  Global stability of a difference equation with maximum , 2009, Appl. Math. Comput..

[4]  L. Berg,et al.  On the asymptotics of the difference equation y n (1 + y n − 1 … y n − k + 1) = y n − k , 2011 .

[5]  Stevo Stević,et al.  Boundedness character of a class of difference equations , 2009 .

[6]  S. Stević.  Nontrivial solutions of a higher-order rational difference equation , 2008 .

[7]  Stevo Stevic,et al.  Periodicity of a class of nonautonomous max-type difference equations , 2011, Appl. Math. Comput..

[8]  Stevo Stević,et al.  Global stability and asymptotics of some classes of rational difference equations , 2006 .

[9]  Stevo Stević,et al.  On a nonlinear generalized max-type difference equation , 2011 .

[10]  Stevo Stevic,et al.  Existence of nontrivial solutions of a rational difference equation , 2007, Appl. Math. Lett..

[11]  Stevo Stevic,et al.  On a class of third-order nonlinear difference equations , 2009, Appl. Math. Comput..

[12]  C. Schinas,et al.  Invariants and oscillation for systems of two nonlinear difference equations , 2001 .

[13]  Stevo Stevic.  On the difference equation xn+1=alpha + xn-1/xn , 2008, Comput. Math. Appl..

[14]  Lothar Berg,et al.  Linear difference equations mod 2 with applications to nonlinear difference equations1 , 2008 .

[15]  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 .

[16]  Cengiz Çinar,et al.  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) , 2011, Math. Comput. Model..

[17]  Stevo Stevic,et al.  On the recursive sequence xn+1 = max{c, xpn/xpn-1} , 2008, Appl. Math. Lett..

[18]  Kenneth S. Berenhaut,et al.  The global attractivity of a higher order rational difference equation , 2007 .

[19]  Kenneth S. Berenhaut,et al.  The behaviour of the positive solutions of the difference equation , 2006 .

[20]  Marwan Aloqeili.  Global stability of a rational symmetric difference equation , 2009, Appl. Math. Comput..

[21]  G. Papaschinopoulos,et al.  Trichotomy of a system of two difference equations , 2004 .

[22]  Lothar Berg,et al.  Periodicity of some classes of holomorphic difference equations , 2006 .

[23]  Stevo Stevi´c,et al.  ON THE RECURSIVE SEQUENCE $x_{n+1}=x_{n-1}/g(x_n)$ , 2002 .

[24]  G. Ladas,et al.  On the Recursive Sequencexn + 1 = α + xn − 1/xn☆ , 1999 .

[25]  Stevo Stevic,et al.  Eventually constant solutions of a rational difference equation , 2009, Appl. Math. Comput..

[26]  Stevo Stević,et al.  A short proof of the Cushing-Henson conjecture , 2006 .

[27]  Stevo Stevic,et al.  Global stability of a max-type difference equation , 2010, Appl. Math. Comput..

[28]  Josef Diblík,et al.  Asymptotically periodic solutions of Volterra system of difference equations , 2010, Comput. Math. Appl..

[29]  Stevo Stevic,et al.  On positive solutions of a (k+1)th order difference equation , 2006, Appl. Math. Lett..

[30]  Stevo Stević,et al.  On a generalized max-type difference equation from automatic control theory , 2010 .

[31]  Kenneth S. Berenhaut,et al.  The global attractivity of the rational difference equation _{}=1+\frac{_{-}}_{-} , 2007 .