Qualitative Properties of Difference Equation of Order Six

Abdul Khaliq and E.M. Elsayed
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Abdul 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, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2016, vol. 4, issue 2, 1-14

Abstract: In this paper we study the qualitative properties and the periodic nature of the solutions of the difference equation x n + 1 = ? x n - 2 + ? x n - 2 2 ? x n - 2 + ? 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 ? , ? , ? , ? are positive constants. In addition, we derive the form of the solutions of some special cases of this equation.

Keywords: periodicity; global attractor; boundedness; rational difference equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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