Global Attractivity and Periodic Character of Difference Equation of Order Four. (31st October 2012)

• Record Type: Journal Article
• Authors: Obaid, M. A.; Elsayed, E. M.; El-Dessoky, M. M.
• Other Names: Yalcinkaya Ibrahim Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2012(2012)
• Publication Date: 2012-10-31
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2012/746738
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : We investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence x n + 1 = a x n + ( ( b x n - 1 + c x n - 2 + d x n - 3 ) / ( α x n - 1 + β x n - 2 + γ x n - 3 ) ), n = 0, 1, …, where the parameters a, b, c, d, α, β, and γ are positive real numbers and the initial conditions x - 3, x - 2, x - 1, and x 0 are positive real numbers.