Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and 2k-Periodic Coefficients. (22nd April 2015)

• Record Type: Journal Article
• Authors: Dou, Liping; Hou, Chengmin; Cheng, Sui Sun
• Other Names: Papashinopoulos Garyfalos Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2015(2015)
• Publication Date: 2015-04-22
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2015/610345
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : A nonlinear recurrence involving a piecewise constant McCulloch-Pitts function and2 k -periodic coefficient sequences is investigated. By allowing the threshold parameter to vary from 0 to∞, we work out a complete bifurcation analysis for the asymptotic behaviors of the corresponding solutions. Among other things, we show that each solution tends towards one of four different limits. Furthermore, the accompanying initial regions for each type of solutions can be determined. It is hoped that our analysis will provide motivation for further results for recurrent McCulloch-Pitts type neural networks.