On the periodicity of the solution of a rational difference equation

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

___

  • 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.