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Qualitative Properties of Difference Equation of Order Six

Author

Listed:
  • 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
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

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.

Suggested Citation

  • Abdul Khaliq & E.M. Elsayed, 2016. "Qualitative Properties of Difference Equation of Order Six," Mathematics, MDPI, vol. 4(2), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:2:p:24-:d:68017
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    References listed on IDEAS

    as
    1. E. M. Elsayed, 2011. "Solution and Attractivity for a Rational Recursive Sequence," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-17, June.
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