A weak condition for global stability of delayed neural networks
The classical analysis of asymptotical and exponential stability of neural networks needs assumptions on the existence of a positive Lyapunov function V and on the strict negativity of the function dV=dt, which often come as a result of boundedness or uniformly almost periodicity of the activation f...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Published: |
American Institute of Mathematical Sciences (A I M S Press)
2016
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| Online Access: | http://hdl.handle.net/20.500.11937/40445 |
| _version_ | 1848755873221967872 |
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| author | Luo, R. Xu, Honglei Wang, W. Sun, Jie Xu, W. |
| author_facet | Luo, R. Xu, Honglei Wang, W. Sun, Jie Xu, W. |
| author_sort | Luo, R. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The classical analysis of asymptotical and exponential stability of neural networks needs assumptions on the existence of a positive Lyapunov function V and on the strict negativity of the function dV=dt, which often come as a result of boundedness or uniformly almost periodicity of the activation functions. In this paper, we investigate the asymptotical stability problem of Hopfield neural networks with time delays under weaker conditions. By constructing a suitable Lyapunov function, sufficient conditions are derived to guarantee global asymptotical stability and exponential stability of the equilibrium of the system. These conditions do not require the strict negativity of dV=dt, nor do they require that the activation functions to be bounded or uniformly almost periodic. |
| first_indexed | 2025-11-14T09:03:13Z |
| format | Journal Article |
| id | curtin-20.500.11937-40445 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:03:13Z |
| publishDate | 2016 |
| publisher | American Institute of Mathematical Sciences (A I M S Press) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-404452017-09-13T13:37:32Z A weak condition for global stability of delayed neural networks Luo, R. Xu, Honglei Wang, W. Sun, Jie Xu, W. The classical analysis of asymptotical and exponential stability of neural networks needs assumptions on the existence of a positive Lyapunov function V and on the strict negativity of the function dV=dt, which often come as a result of boundedness or uniformly almost periodicity of the activation functions. In this paper, we investigate the asymptotical stability problem of Hopfield neural networks with time delays under weaker conditions. By constructing a suitable Lyapunov function, sufficient conditions are derived to guarantee global asymptotical stability and exponential stability of the equilibrium of the system. These conditions do not require the strict negativity of dV=dt, nor do they require that the activation functions to be bounded or uniformly almost periodic. 2016 Journal Article http://hdl.handle.net/20.500.11937/40445 10.3934/jimo.2016.12.505 American Institute of Mathematical Sciences (A I M S Press) unknown |
| spellingShingle | Luo, R. Xu, Honglei Wang, W. Sun, Jie Xu, W. A weak condition for global stability of delayed neural networks |
| title | A weak condition for global stability of delayed neural networks |
| title_full | A weak condition for global stability of delayed neural networks |
| title_fullStr | A weak condition for global stability of delayed neural networks |
| title_full_unstemmed | A weak condition for global stability of delayed neural networks |
| title_short | A weak condition for global stability of delayed neural networks |
| title_sort | weak condition for global stability of delayed neural networks |
| url | http://hdl.handle.net/20.500.11937/40445 |