Global attractivity in a recursive sequence

In this paper, we study the invariant intervals, the globally attractivity of the two equilibrium points, and the oscillatory behavior of the solutions of the difference equationx"n=ax"n"-"1-bx"n"-"2c+x"n"-"2,n=1,2,...,where a,b,c>0.

[1]  B. Shi,et al.  A rational recursive sequence , 2001 .

[2]  Wan-Tong Li,et al.  Global attractivity for a class of higher order nonlinear difference equations , 2004, Appl. Math. Comput..

[3]  H. M. El-Owaidy,et al.  On asymptotic behaviour of the difference equation xn+1=α+(xn-k/xn) , 2004, Appl. Math. Comput..

[4]  Hong-Jian Lai,et al.  Global asymptotic stability in a rational recursive sequence , 2004, Appl. Math. Comput..

[5]  Long Li.  Stability properties of nonlinear difference equations and conditions for boundedness , 1999 .

[6]  H. M. El-Owaidy,et al.  On the recursive sequences xn+1=-αxn-1/β±xn , 2003, Appl. Math. Comput..

[7]  V. Kocić,et al.  On Rational Recursive Sequences , 1993 .

[8]  Mustafa R. S. Kulenovic,et al.  A rational difference equation , 2001 .

[9]  Wan-Tong Li,et al.  Global attractivity in a rational recursive sequence , 2003, Appl. Math. Comput..

[10]  Raghib M. Abu-Saris,et al.  Global stability of yn+1 = A + yN/yN-k , 2003, Appl. Math. Lett..

[11]  G. Ladas,et al.  On the recursive sequence xn+1=(α+βxn)/(Bxn+Cxn−1) , 2001 .

[12]  M. M. El-Afifi.  On the recursive sequence xn+1=α+βxn+γsn-1/Bxn+Cxn-1 , 2004, Appl. Math. Comput..

[13]  Alaa E. Hamza,et al.  Stability of the recursive sequence xn+1 = (α - βxn)/(γ + xn-1) , 2001 .

[14]  Wan-Tong Li,et al.  Global attractivity in the recursive sequence xn+1=(α-βxn)/(γ-xn-1) , 2003, Appl. Math. Comput..

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

[16]  Wan-Tong Li,et al.  Global attractivity of a higher order nonlinear difference equation , 2005 .

[17]  Mustafa R. S. Kulenovic,et al.  On the Recursive Sequence yn + 1 = (p + yn − 1)/(qyn + yn − 1) , 2000 .

[18]  H.M. El-Owaidy,et al.  A note on the periodic cycle of Xn+2=(1+Xn+1)/(Xn) , 2000, Appl. Math. Comput..

[19]  V. Kocić,et al.  Global Behavior of Nonlinear Difference Equations of Higher Order with Applications , 1993 .