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

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Authors
M. M. ElDessoky
 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.
E. M. Elsayed
 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.
E. O. Alzahrani
 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
Abstract
In this paper, we investigate the expressions of solutions and the periodic nature of the following systems
of rational difference equations with order four
\[x_{n+1} = \frac{y_{n3} }{\pm 1\pm y_nz_{n1}x_{n2}y_{n3}},
y_{n+1} = \frac{z_{n3} }{\pm 1\pm z_nx_{n1}y_{n2}z_{n3}},
z_{n+1} = \frac{x_{n3} }{\pm 1\pm x_ny_{n1}z_{n2}x_{n3}},\]
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.
Share and Cite
ISRP Style
M. M. ElDessoky, E. M. Elsayed, E. O. Alzahrani, The form of solutions and periodic nature for some rational difference equations systems, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 10, 56295647
AMA Style
ElDessoky M. M., Elsayed E. M., Alzahrani E. O., The form of solutions and periodic nature for some rational difference equations systems. J. Nonlinear Sci. Appl. (2016); 9(10):56295647
Chicago/Turabian Style
ElDessoky, M. M., Elsayed, E. M., Alzahrani, E. O.. "The form of solutions and periodic nature for some rational difference equations systems." Journal of Nonlinear Sciences and Applications, 9, no. 10 (2016): 56295647
Keywords
 Difference equations
 recursive sequences
 stability
 periodic solution
 system of difference equations.
MSC
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