Expressions and dynamical behavior of solutions of a class of rational difference equations of fifteenthorder
Authors
A. M. Ahmed
 Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Jouf, Saudi Arabia.
 Department of Mathematics, Faculty of Science, Al Azhar University, Nasr City 11884, Cairo, Egypt.
Samir Al Mohammady
 Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Jouf, Saudi Arabia.
 Department of Mathematics, Faculty of Science, Helwan University, Helwan 11795, Egypt.
Lama Sh. Aljoufi
 Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Jouf, Saudi Arabia.
Abstract
The main goal of this paper, is to obtain the forms of the solutions of the
following nonlinear fifteenthorder difference equations
\[
x_{n+1}=\frac{x_{n14}}{\pm 1\pm x_{n2}x_{n5}x_{n8}x_{n11}x_{n14}},\ \
\ \ n=0,1,2,\ldots,\]
where the initial conditions \(x_{14},x_{13},\ldots,x_{0}\) 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.
Share and Cite
ISRP Style
A. M. Ahmed, Samir Al Mohammady, Lama Sh. Aljoufi, Expressions and dynamical behavior of solutions of a class of rational difference equations of fifteenthorder, Journal of Mathematics and Computer Science, 25 (2022), no. 1, 1022
AMA Style
Ahmed A. M., Mohammady Samir Al, Aljoufi Lama Sh., Expressions and dynamical behavior of solutions of a class of rational difference equations of fifteenthorder. J Math Comput SCIJM. (2022); 25(1):1022
Chicago/Turabian Style
Ahmed, A. M., Mohammady, Samir Al, Aljoufi, Lama Sh.. "Expressions and dynamical behavior of solutions of a class of rational difference equations of fifteenthorder." Journal of Mathematics and Computer Science, 25, no. 1 (2022): 1022
Keywords
 Recursive sequence
 oscillation
 semicycles
 stability
 periodicity
 solutions of difference equations
MSC
References

[1]
R. P. Agarwal, Difference equations and inequalities, Marcel Dekker, New York (2000)

[2]
R. P. Agarwal, E. M. Elsayed, Periodicity and stability of solutions of higher order rational difference equation, Adv. Stud. Contemp. Math., 17 (2008), 181201

[3]
A. M. Ahmed, On the dynamics of a higher order rational difference equation, Discrete Dyn. Nat. Soc., 2011 (2011), 8 pages

[4]
, On the recursive sequence $x_{n+1}=(a+b x_{n1})/(A+B x^k_{n})$, J. Appl. Math. Inform., 27 (2009), 275289

[5]
A. M. Ahmed, A. M. Youssef, A solution form of a class of higherorder rational difference equations, J. Egyptian Math. Soc., 21 (2013), 248253

[6]
M. Aloqeili, Dynamics of a rational difference equation, Appl. Math. Comput., 176 (2006), 768774

[7]
A. M. Amleh, J. Hoag, G. Ladas, A difference equation with eventually periodic solutions, Comput. Math. Appl., 36 (1998), 401404

[8]
C. Cinar, On the positive solutions of the difference equation $x_{n+1}=(x_{n1})/(1+x_nx_{n1})$, Appl. Math. Comput., 150 (2004), 2124

[9]
C. Cinar, On the difference equation $x_{n+1}=\frac{x_{n1}}{1+x_nx_{n1}}$, Appl. Math. Comput., 158 (2004), 813816

[10]
C. Cinar, On the positive solutions of the difference equation $x_{n+1}=\frac{ax_{n1}}{1+bx_n x_{n1}}$, Appl. Math. Comput., 156 (2004), 587590

[11]
R. Devault, V. L. Kocic, D. Stutson, Global behavior of solutions of the nonlinear difference equation $x_{n+1}=p_n+x_{n1}/x_n$, J. Difference Equ. Appl., 11 (2005), 707719

[12]
E. M. Elsayed, On the difference equation $x_{n+1}=\frac{x_{n5}}{1+x_{n2}x_{n5}}$, Int. J. Contemp. Math. Sci., 3 (2008), 16571664

[13]
E. M. Elsayed, M. A. Marwa, Expressions and dynamical behavior of rational recursive sequences, J. Comput. Anal. Appl.,, 28 (2020), 6778

[14]
E. A. Grove, G. Ladas, Periodicities in nonlinear difference equations, Chapman & Hall/CRC, Boca Raton (2005)

[15]
R. Karatas, C. Cinar, D. Simsek, On positive solutions of the difference equation $x_{n+1}=\frac{x_{n5}}{1+x_{n2}x_{n5}}$, Int. J. Contemp. Math. Sci., 1 (2006), 495500

[16]
V. L. Kocic, G. Ladas, Global behavior of nonlinear difference equations of higher order with applications, Kluwer Academic Publishers, Dordrecht (1993)

[17]
M. R. S. Kulenovic, G. Ladas, Dynamics of second order rational difference equations with open problems and conjectures, Chapman & Hall/CRC, Florida (2001)