Global attractivity of a rational difference equation of order ten

Volume 9, Issue 6, pp 4465--4477 http://dx.doi.org/10.22436/jnsa.009.06.85

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Authors

Abdul Khaliq - Riphah Institute of Computing Applied Sciences (RICAS), Department of Mathematics, Riphah International University, Lahore Campus.. Faris Alzahrani - Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. E. M. Elsayed - Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. - Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.

Abstract

In this paper, we study qualitative properties and periodic nature of the solutions of the difference equation \[x_{n+1} = ax_{n-4} +\frac{ bx^2_{ n-4}}{ cx_{n-4} + dx_{n-9}} ; \qquad n = 0; 1; ...;\] where the initial conditions \(x_{-9}; x_{-8}; x_{-7}; x_{-6}; x_{-5}; x_{-4}; x_{-3}; x_{-2}; x_{-1}; x_0\) are arbitrary positive real numbers and \(a; b; c; d\) are constants. Also we obtain the form of solutions of some special cases of this equation.

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Keywords

• Periodicity
• stability
• rational difference equations.

MSC

•  39A10

References

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