On the solutions and periodicity of some nonlinear systems of difference equations

Volume 9, Issue 5, pp 2190--2207 http://dx.doi.org/10.22436/jnsa.009.05.23

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Authors

M. M. El-Dessoky - Faculty of Science, Mathematics Department, King AbdulAziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.

Abstract

We investigate the expressions of solutions and the periodicity nature of the following system of rational difference equations of order four \[x_{n+1 }= \frac{z_{n-3}}{ a_1 + b_1z_ny_{n-1}x_{n-2}z_{n-3}}, y_{n+1 }= \frac{x_{n-3}}{ a_2 + b_2x_nz_{n-1}y_{n-2}x_{n-3}},\] \[z_{n+1 }= \frac{y_{n-3}}{ a_3 + b_3y_nx_{n-1}z_{n-2}y_{n-3}},\] where the 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 \(z_0\) are arbitrary real numbers and \(a_1; b_1; a_2; b_2; a_3; b_3\) are integers.

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Keywords

• System of difference equations
• recursive sequences
• stability
• periodic solution
• solution of difference equation.

MSC

•  39A10
•  39A22
•  39A23

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