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- Title
Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and 2k-Periodic Coefficients.
- Authors
Dou, Liping; Hou, Chengmin; Cheng, Sui Sun
- Abstract
A nonlinear recurrence involving a piecewise constant McCulloch-Pitts function and 2k-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.
- Subjects
BIFURCATION theory; NONLINEAR theories; COEFFICIENTS (Statistics); PARAMETERS (Statistics); ARTIFICIAL neural networks
- Publication
Discrete Dynamics in Nature & Society, 2015, Vol 2015, p1
- ISSN
1026-0226
- Publication type
Article
- DOI
10.1155/2015/610345