Dynamical Properties in a Fourth-OrderNonlinear Difference Equation. (9th May 2010)

• Record Type: Journal Article
• Authors: Chen, Yunxin; Li, Xianyi
• Other Names: Yu Jianshe S. Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2010(2010)
• Publication Date: 2010-05-09
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2010/679409
• Languages: English
• ISSNs: 1687-1847

Abstract

Abstract : The rule of trajectory structure for fourth-order nonlinear difference equationx n + 1 = (x a n − 2 + x n − 3) / (x a n − 2 x n − 3 + 1), n = 0, 1, 2, …, wherea ∈ [ 0, 1 ) and the initial valuesx − 3, x − 2, x − 1, x 0 ∈ [ 0, ∞ ), is described clearly out in this paper. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is4 +, 3 −, 1 +, 2 −, 2 +, 1 −, 1 +, 1 − in a period. By utilizing this rule its positive equilibrium point is verified to be globally asymptotically stable.