Expressions and dynamical behavior of solutions of a class of rational difference equations of fifteenth-order

The main goal of this paper, is to obtain the forms of the solutions of the following nonlinear fifteenth-order difference equations xn+1 = xn−14 ±1± xn−2xn−5xn−8xn−11xn−14 , n = 0, 1, 2, . . . , where the initial conditions x−14, x−13, . . . , x0 are arbitrary real numbers. Moreover, we investigate stability, boundedness, oscillation and the periodic character of these solutions. Finally, we confirm the results with some numerical examples and graphs by using Matlab program.

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

[2]  A. M. Ahmed,et al.  A solution form of a class of higher-order rational difference equations , 2013 .

[3]  G. Ladas,et al.  A difference equation with eventually periodic solutions , 1998 .

[4]  Cengiz Cinar,et al.  On the positive solutions of the difference equation xn+1=(xn-1)/(1+xnxn-1) , 2004, Appl. Math. Comput..

[5]  Alaa E. Hamza,et al.  On the recursive sequence x n+1 =.... , 2008 .

[6]  E. Elsayed.  On the Difference Equation xn + 1 = xn − 5 − 1 + xn − 2 xn − 5 , 2008 .

[7]  R. DeVault,et al.  Global behavior of solutions of the nonlinear difference equation , 2005 .

[8]  G. Ladas,et al.  Periodicities in Nonlinear Difference Equations , 2004 .

[9]  M. A. El-Moneam,et al.  Dynamics of the Rational Difference Equation , 2014 .

[10]  M. Starke,et al.  How to be positive , 2020, Glossa: a journal of general linguistics.

[11]  Mehdi Dehghan,et al.  Dynamics of a higher-order rational difference equation , 2006, Appl. Math. Comput..

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

[13]  E. Camouzis,et al.  Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures , 2001 .

[14]  Ravi P. Agarwal,et al.  Difference equations and inequalities , 1992 .

[15]  C. J. Schinas,et al.  On the Recursive Sequence xn 1 A , 2009 .

[16]  C. Çinar,et al.  On Positive Solutions of the Difference Equation xn , 2006 .

[17]  Cengiz Cinar,et al.  On the positive solutions of the difference equation xn+1 = (axn-1) / (1+bnnxn-1) , 2004, Appl. Math. Comput..