Bifurcation in a Discrete-Time Piecewise Constant Dynamical System
The study of recurrent neural networks with piecewise constant transition or control functions has attracted much attention recently because they can be used to simulate many physical phenomena. A recurrent and discontinuous two-state dynamical system involving a nonnegative bifurcation parameter is...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/492014 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850110404761485312 |
|---|---|
| author | Chenmin Hou Sui Sun Cheng |
| author_facet | Chenmin Hou Sui Sun Cheng |
| author_sort | Chenmin Hou |
| collection | DOAJ |
| description | The study of recurrent neural networks with piecewise constant transition or control functions has attracted much attention recently because they can be used to simulate many physical phenomena. A recurrent and discontinuous two-state dynamical system involving a nonnegative bifurcation parameter is studied. By elementary but novel arguments, we are able to give a complete analysis on its asymptotic behavior when the parameter varies from 0 to . It is hoped that our analysis will provide motivation for further results on large-scale recurrent McCulloch-Pitts-type neural networks and piecewise continuous discrete-time dynamical systems. |
| format | Article |
| id | doaj-art-421f0874f8b9435db2d70b9e3aa31767 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-421f0874f8b9435db2d70b9e3aa317672025-08-20T02:37:51ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/492014492014Bifurcation in a Discrete-Time Piecewise Constant Dynamical SystemChenmin Hou0Sui Sun Cheng1Department of Mathematics, Yanbian University, Yanji 133002, ChinaDepartment of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, ChinaThe study of recurrent neural networks with piecewise constant transition or control functions has attracted much attention recently because they can be used to simulate many physical phenomena. A recurrent and discontinuous two-state dynamical system involving a nonnegative bifurcation parameter is studied. By elementary but novel arguments, we are able to give a complete analysis on its asymptotic behavior when the parameter varies from 0 to . It is hoped that our analysis will provide motivation for further results on large-scale recurrent McCulloch-Pitts-type neural networks and piecewise continuous discrete-time dynamical systems.http://dx.doi.org/10.1155/2013/492014 |
| spellingShingle | Chenmin Hou Sui Sun Cheng Bifurcation in a Discrete-Time Piecewise Constant Dynamical System Discrete Dynamics in Nature and Society |
| title | Bifurcation in a Discrete-Time Piecewise Constant Dynamical System |
| title_full | Bifurcation in a Discrete-Time Piecewise Constant Dynamical System |
| title_fullStr | Bifurcation in a Discrete-Time Piecewise Constant Dynamical System |
| title_full_unstemmed | Bifurcation in a Discrete-Time Piecewise Constant Dynamical System |
| title_short | Bifurcation in a Discrete-Time Piecewise Constant Dynamical System |
| title_sort | bifurcation in a discrete time piecewise constant dynamical system |
| url | http://dx.doi.org/10.1155/2013/492014 |
| work_keys_str_mv | AT chenminhou bifurcationinadiscretetimepiecewiseconstantdynamicalsystem AT suisuncheng bifurcationinadiscretetimepiecewiseconstantdynamicalsystem |