On the dynamics of a higher-order difference equation

Abstract

This paper deals with the investigation of the following more general rational difference equation: y n + 1 = y n / (β +γσ i = 0k y n - (2 i + 1)πi ∈= 0 ki=0n - (2 i + 1)), n = 0,1, 2, , where α,β,γ,p ∈ (0,∞ ) with the initial conditions x 0, x - 1, , x - 2 k, x - 2 k - 1 ∈(0,∞ ). We investigate the existence of the equilibrium points of the considered equation and then study their local and global stability. Also, some results related to the oscillation and the permanence of the considered equation have been presented. Copyright © 2012 H. El-Metwally.