Dynamics of a Higher-Order System of Difference Equations. (19th January 2017)

• Record Type: Journal Article
• Authors: Wang, Qi; Zhang, Qinqin; Li, Qirui
• Other Names: Peterson Allan C. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2017(2017)
• Publication Date: 2017-01-19
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2017/4312640
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : Consider the following system of difference equations: x n + 1 ( i ) = x n - m + 1 ( i ) / A i ∏ j = 0 m - 1 x n - j ( i + j + 1 ) + α i, x n + 1 ( i + m ) = x n + 1 ( i ), x 1 - l ( i + l ) = a i, l, A i + m = A i, α i + m = α i, i, l = 1, 2, …, m ; n = 0, 1, 2, …, where m is a positive integer, A i, α i, i = 1, 2, …, m, and the initial conditions a i, l, i, l = 1, 2, …, m, are positive real numbers. We obtain the expressions of the positive solutions of the system and then give a precise description of the convergence of the positive solutions. Finally, we give some numerical results.