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Copyright © 2015 Liping Dou et al. Liping Dou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A nonlinear recurrence involving a piecewise constant McCulloch-Pitts function and 2 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.

Details

Title
Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and 2 k -Periodic Coefficients
Author
Dou, Liping; Hou, Chengmin; Sui Sun Cheng
Publication year
2015
Publication date
2015
Publisher
John Wiley & Sons, Inc.
ISSN
10260226
e-ISSN
1607887X
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
1677804827
Copyright
Copyright © 2015 Liping Dou et al. Liping Dou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.