Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms
The stability issue is investigated for a class of stochastic neural networks with time delays in the leakage terms. Different from the previous literature, we are concerned with the almost sure stability. By using the LaSalle invariant principle of stochastic delay differential equations, Itô’s for...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/2487957 |
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| _version_ | 1832562503784071168 |
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| author | Mingzhu Song Quanxin Zhu Hongwei Zhou |
| author_facet | Mingzhu Song Quanxin Zhu Hongwei Zhou |
| author_sort | Mingzhu Song |
| collection | DOAJ |
| description | The stability issue is investigated for a class of stochastic neural networks with time delays in the leakage terms. Different from the previous literature, we are concerned with the almost sure stability. By using the LaSalle invariant principle of stochastic delay differential equations, Itô’s formula, and stochastic analysis theory, some novel sufficient conditions are derived to guarantee the almost sure stability of the equilibrium point. In particular, the weak infinitesimal operator of Lyapunov functions in this paper is not required to be negative, which is necessary in the study of the traditional moment stability. Finally, two numerical examples and their simulations are provided to show the effectiveness of the theoretical results and demonstrate that time delays in the leakage terms do contribute to the stability of stochastic neural networks. |
| format | Article |
| id | doaj-art-dd7fc9d5952a4f3b81f649ef9b6364cf |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-dd7fc9d5952a4f3b81f649ef9b6364cf2025-02-03T01:22:31ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/24879572487957Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage TermsMingzhu Song0Quanxin Zhu1Hongwei Zhou2Department of Mathematics and Computer Science, Tongling University, Tongling 244000, ChinaSchool of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing 210023, ChinaSchool of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing, Jiangsu 211171, ChinaThe stability issue is investigated for a class of stochastic neural networks with time delays in the leakage terms. Different from the previous literature, we are concerned with the almost sure stability. By using the LaSalle invariant principle of stochastic delay differential equations, Itô’s formula, and stochastic analysis theory, some novel sufficient conditions are derived to guarantee the almost sure stability of the equilibrium point. In particular, the weak infinitesimal operator of Lyapunov functions in this paper is not required to be negative, which is necessary in the study of the traditional moment stability. Finally, two numerical examples and their simulations are provided to show the effectiveness of the theoretical results and demonstrate that time delays in the leakage terms do contribute to the stability of stochastic neural networks.http://dx.doi.org/10.1155/2016/2487957 |
| spellingShingle | Mingzhu Song Quanxin Zhu Hongwei Zhou Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms Discrete Dynamics in Nature and Society |
| title | Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms |
| title_full | Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms |
| title_fullStr | Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms |
| title_full_unstemmed | Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms |
| title_short | Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms |
| title_sort | almost sure stability of stochastic neural networks with time delays in the leakage terms |
| url | http://dx.doi.org/10.1155/2016/2487957 |
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