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Year 2019, Volume: 68 Issue: 2, 1427 - 1434, 01.08.2019
https://doi.org/10.31801/cfsuasmas.535865

Abstract

References

  • Abdul, Khaliq, Faris, Alzahrani and Elsayed, E. M., Global attractivity of a rational difference equation of order ten, Journal of Nonlinear Sciences and Applications, 9 (2016), 4465--4477.
  • Alotaibi, A. M., El-Moneam, M. A. and Noorani, M. S. M., On the rational difference equation y_{n+1}=((α₀y_{n}+α₁y_{n-p}+α₂y_{n-q}+α₃y_{ n-r}+α₄y_{n-s})/(β₀y_{n}+β₁y_{n-p}+β₂y_{n-q}+β₃y_{n-r}+β₄y_{n-s})), Journal of Nonlinear Sciences and Applications, 11 (2018), 80--97.
  • Alotaibi, A. M., Noorani M. S. M. and El-Moneam, M. A., On the Asymptotic Behavior Of Some Nonlinear Difference Equations, Journal of Computational Analysis and Applications, 26 (2019), 604--627.
  • El-Moneam, M. A. and Alamoudy, S. O., On study of the asymptotic behavior of some rational difference equations, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysi, 21 (2014), 89--109.
  • El-Moneam, M. A., On the dynamics of the higher order nonlinear rational difference equation, Mathematical Sciences Letter, 3 (2014) 121--129.
  • Elsayed, E. M., On the global attractivity and periodic character of a recursive sequence, Opuscula Mathematica, 30 (2010), 431--446.
  • Grove, E. A. and Ladas, G., Periodicities in nonlinear difference equations, Vol.4, Chapman & Hall / CRC, 2005.
  • Ibrahim, T. F., Periodicity and global attractivity of difference equation of higher order. Journal of Computational Analysis and Applications, 16 (2014).
  • Ocalan, O., Global dynamics of a non-autonomous rational difference equation. Journal of Applied Mathematics &Informatics, 32, (2014) 843--848.
  • Touafek, N. and Elsayed, E. M., On the periodicity of some systems of nonlinear difference equations, Bulletin mathematique de la Sociat des Sciences Mathematiques de Roumanie, 55, (2012), 217--224.

On the periodicity of the solution of a rational difference equation

Year 2019, Volume: 68 Issue: 2, 1427 - 1434, 01.08.2019
https://doi.org/10.31801/cfsuasmas.535865

Abstract

In this paper, some cases on the periodicity of the rational difference equation

S_{n+1}=S_{n-p}(((aS_{n-q}+bS_{n-r}+cS_{n-s})/(dS_{n-q}+eS_{ n-r}+fS_{n-s}))),

are investigated, where a, b, c, d, e, f ∈(0,∞). The initial conditions S_{-p}, S_{-p+1},...,S_{-q},  S_{-q+1},...,S_{-r},  S_{-r+1},...,S_{-s},...,S_{-s+1},...,S₋₁ and S₀ are arbitrary positive real numbers such that p>q>r>s≥0. Some numerical examples are provided to illustrate the theoretical discussion.

References

  • Abdul, Khaliq, Faris, Alzahrani and Elsayed, E. M., Global attractivity of a rational difference equation of order ten, Journal of Nonlinear Sciences and Applications, 9 (2016), 4465--4477.
  • Alotaibi, A. M., El-Moneam, M. A. and Noorani, M. S. M., On the rational difference equation y_{n+1}=((α₀y_{n}+α₁y_{n-p}+α₂y_{n-q}+α₃y_{ n-r}+α₄y_{n-s})/(β₀y_{n}+β₁y_{n-p}+β₂y_{n-q}+β₃y_{n-r}+β₄y_{n-s})), Journal of Nonlinear Sciences and Applications, 11 (2018), 80--97.
  • Alotaibi, A. M., Noorani M. S. M. and El-Moneam, M. A., On the Asymptotic Behavior Of Some Nonlinear Difference Equations, Journal of Computational Analysis and Applications, 26 (2019), 604--627.
  • El-Moneam, M. A. and Alamoudy, S. O., On study of the asymptotic behavior of some rational difference equations, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysi, 21 (2014), 89--109.
  • El-Moneam, M. A., On the dynamics of the higher order nonlinear rational difference equation, Mathematical Sciences Letter, 3 (2014) 121--129.
  • Elsayed, E. M., On the global attractivity and periodic character of a recursive sequence, Opuscula Mathematica, 30 (2010), 431--446.
  • Grove, E. A. and Ladas, G., Periodicities in nonlinear difference equations, Vol.4, Chapman & Hall / CRC, 2005.
  • Ibrahim, T. F., Periodicity and global attractivity of difference equation of higher order. Journal of Computational Analysis and Applications, 16 (2014).
  • Ocalan, O., Global dynamics of a non-autonomous rational difference equation. Journal of Applied Mathematics &Informatics, 32, (2014) 843--848.
  • Touafek, N. and Elsayed, E. M., On the periodicity of some systems of nonlinear difference equations, Bulletin mathematique de la Sociat des Sciences Mathematiques de Roumanie, 55, (2012), 217--224.
There are 10 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

A. M. Alotaibi 0000-0002-0516-1933

M. S. M. Noorani

M. A. El-moneam 0000-0002-1676-2662

Publication Date August 1, 2019
Submission Date August 20, 2018
Acceptance Date January 13, 2019
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Alotaibi, A. M., Noorani, M. S. M., & El-moneam, M. A. (2019). On the periodicity of the solution of a rational difference equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1427-1434. https://doi.org/10.31801/cfsuasmas.535865
AMA Alotaibi AM, Noorani MSM, El-moneam MA. On the periodicity of the solution of a rational difference equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1427-1434. doi:10.31801/cfsuasmas.535865
Chicago Alotaibi, A. M., M. S. M. Noorani, and M. A. El-moneam. “On the Periodicity of the Solution of a Rational Difference Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1427-34. https://doi.org/10.31801/cfsuasmas.535865.
EndNote Alotaibi AM, Noorani MSM, El-moneam MA (August 1, 2019) On the periodicity of the solution of a rational difference equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1427–1434.
IEEE A. M. Alotaibi, M. S. M. Noorani, and M. A. El-moneam, “On the periodicity of the solution of a rational difference equation”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1427–1434, 2019, doi: 10.31801/cfsuasmas.535865.
ISNAD Alotaibi, A. M. et al. “On the Periodicity of the Solution of a Rational Difference Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1427-1434. https://doi.org/10.31801/cfsuasmas.535865.
JAMA Alotaibi AM, Noorani MSM, El-moneam MA. On the periodicity of the solution of a rational difference equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1427–1434.
MLA Alotaibi, A. M. et al. “On the Periodicity of the Solution of a Rational Difference Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1427-34, doi:10.31801/cfsuasmas.535865.
Vancouver Alotaibi AM, Noorani MSM, El-moneam MA. On the periodicity of the solution of a rational difference equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1427-34.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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