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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 610345, 13 pages
http://dx.doi.org/10.1155/2015/610345
Research Article

Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and -Periodic Coefficients

1Department of Mathematics, Yanbian University, Yanji 133002, China
2Department of Mathematics, Tsing Hua University, Hsinchu 30043, Taiwan

Received 18 January 2015; Revised 10 March 2015; Accepted 11 March 2015

Academic Editor: Garyfalos Papashinopoulos

Copyright © 2015 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 -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.