The Dynamics and Solution of some Difference Equations
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Authors
A. Khaliq
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
E. M. Elsayed
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
- Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
Abstract
In this paper, we study solution and periodic nature of the following difference equations
\[x_{n+1} =\frac{
x_{n-1}x_{n-5}}{
x_{n-3}(\pm 1 \pm x_{n-1}x_{n-5})}
;\quad n = 0; 1; ...;\]
where the initial conditions \(x_{-5}; x_{-4}; x_{-3}; x_{-2}; x_{-1}; x_0\) are arbitrary positive real numbers. we studied the
equilibrium points of the given equation. Some qualitative properties such as the global stability, and the
periodic character of the solutions in each case have been studied. We presented some numerical examples
by using random initial values and the coefficients of each case. Some figures have been given to explain
the behavior of the obtained solutions by using MATLAB to confirm the obtained results.
Share and Cite
ISRP Style
A. Khaliq, E. M. Elsayed, The Dynamics and Solution of some Difference Equations, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 3, 1052--1063
AMA Style
Khaliq A., Elsayed E. M., The Dynamics and Solution of some Difference Equations. J. Nonlinear Sci. Appl. (2016); 9(3):1052--1063
Chicago/Turabian Style
Khaliq, A., Elsayed, E. M.. "The Dynamics and Solution of some Difference Equations." Journal of Nonlinear Sciences and Applications, 9, no. 3 (2016): 1052--1063
Keywords
- Periodicity
- stability
- rational difference equations.
MSC
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