On the Periodicity of a Difference Equation with Maximum. (1st June 2008)

• Record Type: Journal Article
• Authors: Gelisken, Ali; Cinar, Cengiz; Yalcinkaya, Ibrahim
• Other Names: Zhou Yong Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2008(2008)
• Publication Date: 2008-06-01
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2008/820629
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : We investigate the periodic nature of solutions of the max difference equationx n + 1 = max ⁡ { x n, A } / ( x n x n − 1 ), n = 0, 1, …, whereA is a positive real parameter, and the initial conditionsx − 1 = A r − 1 andx 0 = A r 0 such thatr − 1 andr 0 are positive rational numbers. The results in this paper answer the Open Problem 6.2 posed by Grove and Ladas (2005).