The Dynamics and Solution of some Difference Equations

Volume 9, Issue 3, pp 1052--1063 http://dx.doi.org/10.22436/jnsa.009.03.33

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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.

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Keywords

• Periodicity
• stability
• rational difference equations.

MSC

•  39A10

References

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