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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| _version_ | 1841524518829424640 |
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| author | Liping Dou Chengmin Hou Sui Sun Cheng |
| author_facet | Liping Dou Chengmin Hou Sui Sun Cheng |
| author_sort | Liping Dou |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-243f37e820f74b24a4a6c32433eac9d6 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-243f37e820f74b24a4a6c32433eac9d62025-02-03T05:53:00ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/610345610345Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and 2k-Periodic CoefficientsLiping Dou0Chengmin Hou1Sui Sun Cheng2Department of Mathematics, Yanbian University, Yanji 133002, ChinaDepartment of Mathematics, Yanbian University, Yanji 133002, ChinaDepartment of Mathematics, Tsing Hua University, Hsinchu 30043, TaiwanA 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.http://dx.doi.org/10.1155/2015/610345 |
| spellingShingle | Liping Dou Chengmin Hou Sui Sun Cheng Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and 2k-Periodic Coefficients Discrete Dynamics in Nature and Society |
| title | Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and 2k-Periodic Coefficients |
| title_full | Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and 2k-Periodic Coefficients |
| title_fullStr | Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and 2k-Periodic Coefficients |
| title_full_unstemmed | Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and 2k-Periodic Coefficients |
| title_short | Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and 2k-Periodic Coefficients |
| title_sort | bifurcation analysis for nonlinear recurrence relations with threshold control and 2k periodic coefficients |
| url | http://dx.doi.org/10.1155/2015/610345 |
| work_keys_str_mv | AT lipingdou bifurcationanalysisfornonlinearrecurrencerelationswiththresholdcontroland2kperiodiccoefficients AT chengminhou bifurcationanalysisfornonlinearrecurrencerelationswiththresholdcontroland2kperiodiccoefficients AT suisuncheng bifurcationanalysisfornonlinearrecurrencerelationswiththresholdcontroland2kperiodiccoefficients |