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Mathematics 2016, 4(2), 24; doi:10.3390/math4020024

Qualitative Properties of Difference Equation of Order Six

1
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
*
Author to whom correspondence should be addressed.
Academic Editor: Johnny Henderson
Received: 10 February 2016 / Revised: 28 March 2016 / Accepted: 1 April 2016 / Published: 12 April 2016
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Abstract

In this paper we study the qualitative properties and the periodic nature of the solutions of the difference equation x n + 1 = α x n - 2 + β x n - 2 2 γ x n - 2 + δ x n - 5 , n = 0 , 1 , . . . , where the initial conditions x - 5 , x - 4 , x - 3 , x - 2 , x - 1 , x 0 are arbitrary positive real numbers and α , β , γ , δ are positive constants. In addition, we derive the form of the solutions of some special cases of this equation. View Full-Text
Keywords: periodicity; global attractor; boundedness; rational difference equations periodicity; global attractor; boundedness; rational difference equations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Khaliq, A.; Elsayed, E. Qualitative Properties of Difference Equation of Order Six. Mathematics 2016, 4, 24.

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