Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and 2 k -Periodic Coefficients

A nonlinear recurrence involving a piecewise constant McCulloch-Pittsfunction and 2 k -periodic coefficient sequences is investigated. Byallowing the threshold parameter to vary from 0 to ∞ , we work outa complete bifurcation analysis for the asymptotic behaviors of thecorresponding solutions. Among other things, we show that each solutiontends towards one of four different limits. Furthermore, the accompanying initialregions for each type of solutions can be determined. It is hoped that ouranalysis will provide motivation for further results for recurrentMcCulloch-Pitts type neural networks.