Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and 2k-Periodic Coefficients
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. Amon...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/610345 |
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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |