Global Attractivity in a Discrete Mutualism Model with Infinite Deviating Arguments. (12th February 2017)

• Record Type: Journal Article
• Authors: Xie, Xiangdong; Xue, Yalong; Wu, Runxin
• Other Names: Papashinopoulos Garyfalos Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2017(2017)
• Publication Date: 2017-02-12
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2017/2912147
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : A set of sufficient conditions is obtained for the global attractivity of the following two-species discrete mutualism model with infinite deviating arguments: x 1 ( k + 1 ) = x 1 k exp ⁡ r 1 ( K 1 + α 1 ∑ s = 0 + ∞ J 2 s x 2 k - s ) / ( 1 + ∑ s = 0 + ∞ J 2 s x 2 k - s ) - x 1 k and x 2 ( k + 1 ) = x 2 k exp ⁡ r 2 ( K 2 + α 2 ∑ s = 0 + ∞ J 1 s x 1 k - s ) / ( 1 + ∑ s = 0 + ∞ J 1 s x 1 k - s ) - x 2 k, where r i, K i, α i, i = 1, 2, are all positive constants, ∑ j = 1 + ∞ J i ( n ) = 1, and α i > K i . Our results generalize the main result of Yang et al. (2014).