The form of solutions and periodic nature for some rational difference equations systems

El-Dessoky, M. M.¹ ; Elsayed, E. M.¹ ; Alzahrani, E. O.²

¹ Faculty of Science, Mathematics Department, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia;Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
² Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 10, p. 5629-5647.

Résumé

In this paper, we investigate the expressions of solutions and the periodic nature of the following systems of rational difference equations with order four

$x_{n+1} = \frac{y_{n-3} }{\pm 1\pm y_nz_{n-1}x_{n-2}y_{n-3}}, y_{n+1} = \frac{z_{n-3} }{\pm 1\pm z_nx_{n-1}y_{n-2}z_{n-3}}, z_{n+1} = \frac{x_{n-3} }{\pm 1\pm x_ny_{n-1}z_{n-2}x_{n-3}},$

with initial conditions $x_{-3}; x_{-2}; x_{-1}; x_0; y_{-3}; y_{-2}; y_{-1}; y_0; z_{-3}; z_{-2}; z_{-1}$ and $z_0$ which are arbitrary real numbers.

Détail

DOI : 10.22436/jnsa.009.10.10

Classification : 39A20, 39A23, 39A30
Keywords: Difference equations, recursive sequences, stability, periodic solution, system of difference equations.

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