Global Asymptotic Stability of a Family of Nonlinear Difference Equations. (4th December 2013)

• Record Type: Journal Article
• Authors: Liao, Maoxin
• Other Names: Çinar Cengiz Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2013(2013)
• Publication Date: 2013-12-04
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2013/750852
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : In this note, we consider global asymptotic stability of the following nonlinear difference equation x n = ( ∏ i = 1 v ( x n - k i β i + 1 ) + ∏ i = 1 v ( x n - k i β i - 1 ) ) / ( ∏ i = 1 v ( x n - k i β i + 1 ) - ∏ i = 1 v ( x n - k i β i - 1 ) ), n = 0, 1, …, where k i ∈ ℕ ( i = 1, 2, …, v ), v ≥ 2, β 1 ∈ [ - 1, 1 ], β 2, β 3, …, β v ∈ ( - ∞, + ∞ ), x - m, x - m + 1, …, x - 1 ∈ ( 0, ∞ ), and m = max 1 ≤ i ≤ v { k i } . Our result generalizes the corresponding results in the recent literature and simultaneously conforms to a conjecture in the work by Berenhaut et al. (2007).