The Dynamics of the Solutions of Some Difference Equations. (22nd May 2012)

• Record Type: Journal Article
• Authors: El-Metwally, H.; Alsaedi, R.; Elsayed, E. M.
• Other Names: Yalcinkaya Ibrahim Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2012(2012)
• Publication Date: 2012-05-22
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2012/475038
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : This paper is devoted to investigate the global behavior of the following rational difference equation:y n + 1 = α y n - t / ( β + γ ∑ i = 0 k y n - ( 2 i + 1 ) p ∏ i = 0 k y n - ( 2 i + 1 ) q ), n = 0, 1, 2, …, whereα, β, γ, p, q ∈ ( 0, ∞ ) andk, t ∈ { 0, 1, 2, … } with the initial conditionsx 0, x - 1, …, x - 2 k, x - 2 max { k, t } - 1 ∈ ( 0, ∞ ) . We will find and classify the equilibrium points of the equations under studying and then investigate their local and global stability. Also, we will study the oscillation and the permanence of the considered equations.