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| Title | Convergent dynamics for multistable delayed neural networks |
| Creator | Shih, Chih-Wen 曾睿彬 Tseng, Jui-Pin |
| Contributor | 應數系 |
| Date | 2008-05 |
| Date Issued | 4-Dec-2018 15:42:48 (UTC+8) |
| Summary | This investigation aims at developing a methodology to establish convergence of dynamics for delayed neural network systems with multiple stable equilibria. The present approach is general and can be applied to several network models. We take the Hopfield-type neural networks with both instantaneous and delayed feedbacks to illustrate the idea. We shall construct the complete dynamical scenario which comprises exactly 2n stable equilibria and exactly (3n − 2n) unstable equilibria for the n-neuron network. In addition, it is shown that every solution of the system converges to one of the equilibria as time tends to infinity. The approach is based on employing the geometrical structure of the network system. Positively invariant sets and componentwise dynamical properties are derived under the geometrical configuration. An iteration scheme is subsequently designed to confirm the convergence of dynamics for the system. Two examples with numerical simulations are arranged to illustrate the present theory. |
| Relation | Nonlinearity, Vol.21, pp.2361-2389 |
| Type | article |
| DOI | http://dx.doi.org/10.1088/0951-7715/21/10/009 |
| dc.contributor | 應數系 | |
| dc.creator (作者) | Shih, Chih-Wen | en_US |
| dc.creator (作者) | 曾睿彬 | zh_TW |
| dc.creator (作者) | Tseng, Jui-Pin | en_US |
| dc.date (日期) | 2008-05 | |
| dc.date.accessioned | 4-Dec-2018 15:42:48 (UTC+8) | - |
| dc.date.available | 4-Dec-2018 15:42:48 (UTC+8) | - |
| dc.date.issued (上傳時間) | 4-Dec-2018 15:42:48 (UTC+8) | - |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/121201 | - |
| dc.description.abstract (摘要) | This investigation aims at developing a methodology to establish convergence of dynamics for delayed neural network systems with multiple stable equilibria. The present approach is general and can be applied to several network models. We take the Hopfield-type neural networks with both instantaneous and delayed feedbacks to illustrate the idea. We shall construct the complete dynamical scenario which comprises exactly 2n stable equilibria and exactly (3n − 2n) unstable equilibria for the n-neuron network. In addition, it is shown that every solution of the system converges to one of the equilibria as time tends to infinity. The approach is based on employing the geometrical structure of the network system. Positively invariant sets and componentwise dynamical properties are derived under the geometrical configuration. An iteration scheme is subsequently designed to confirm the convergence of dynamics for the system. Two examples with numerical simulations are arranged to illustrate the present theory. | en_US |
| dc.format.extent | 641098 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.relation (關聯) | Nonlinearity, Vol.21, pp.2361-2389 | |
| dc.title (題名) | Convergent dynamics for multistable delayed neural networks | en_US |
| dc.type (資料類型) | article | |
| dc.identifier.doi (DOI) | 1088/0951-7715/21/10/009 | |
| dc.doi.uri (DOI) | http://dx.doi.org/10.1088/0951-7715/21/10/009 |