Exponential Stability of Stochastic Delayed Neural Networks with Inverse Hölder Activation Functions and Markovian Jump Parameters
The exponential stability issue for a class of stochastic neural networks (SNNs) with Markovian jump parameters, mixed time delays, and α-inverse Hölder activation functions is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. Firstly...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/784107 |
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| _version_ | 1832567390735433728 |
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| author | Yingwei Li Huaiqin Wu |
| author_facet | Yingwei Li Huaiqin Wu |
| author_sort | Yingwei Li |
| collection | DOAJ |
| description | The exponential stability issue for a class of stochastic neural networks (SNNs) with Markovian jump parameters, mixed time delays, and
α-inverse Hölder activation functions is investigated. The jumping parameters are modeled
as a continuous-time finite-state Markov chain. Firstly, based on Brouwer degree
properties, the existence and uniqueness of the equilibrium point for SNNs without noise perturbations are proved. Secondly, by applying the Lyapunov-Krasovskii functional approach, stochastic analysis theory, and linear matrix inequality (LMI) technique, new delay-dependent sufficient criteria are achieved in terms of LMIs to ensure the SNNs with noise perturbations to be globally exponentially stable in the mean square. Finally, two simulation examples are provided to demonstrate the validity of the theoretical results. |
| format | Article |
| id | doaj-art-98b87cd138e74b198da0d64d16fed589 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-98b87cd138e74b198da0d64d16fed5892025-02-03T01:01:34ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/784107784107Exponential Stability of Stochastic Delayed Neural Networks with Inverse Hölder Activation Functions and Markovian Jump ParametersYingwei Li0Huaiqin Wu1College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, ChinaCollege of Science, Yanshan University, Qinhuangdao 066001, ChinaThe exponential stability issue for a class of stochastic neural networks (SNNs) with Markovian jump parameters, mixed time delays, and α-inverse Hölder activation functions is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. Firstly, based on Brouwer degree properties, the existence and uniqueness of the equilibrium point for SNNs without noise perturbations are proved. Secondly, by applying the Lyapunov-Krasovskii functional approach, stochastic analysis theory, and linear matrix inequality (LMI) technique, new delay-dependent sufficient criteria are achieved in terms of LMIs to ensure the SNNs with noise perturbations to be globally exponentially stable in the mean square. Finally, two simulation examples are provided to demonstrate the validity of the theoretical results.http://dx.doi.org/10.1155/2014/784107 |
| spellingShingle | Yingwei Li Huaiqin Wu Exponential Stability of Stochastic Delayed Neural Networks with Inverse Hölder Activation Functions and Markovian Jump Parameters Discrete Dynamics in Nature and Society |
| title | Exponential Stability of Stochastic Delayed Neural Networks with Inverse Hölder Activation Functions and Markovian Jump Parameters |
| title_full | Exponential Stability of Stochastic Delayed Neural Networks with Inverse Hölder Activation Functions and Markovian Jump Parameters |
| title_fullStr | Exponential Stability of Stochastic Delayed Neural Networks with Inverse Hölder Activation Functions and Markovian Jump Parameters |
| title_full_unstemmed | Exponential Stability of Stochastic Delayed Neural Networks with Inverse Hölder Activation Functions and Markovian Jump Parameters |
| title_short | Exponential Stability of Stochastic Delayed Neural Networks with Inverse Hölder Activation Functions and Markovian Jump Parameters |
| title_sort | exponential stability of stochastic delayed neural networks with inverse holder activation functions and markovian jump parameters |
| url | http://dx.doi.org/10.1155/2014/784107 |
| work_keys_str_mv | AT yingweili exponentialstabilityofstochasticdelayedneuralnetworkswithinverseholderactivationfunctionsandmarkovianjumpparameters AT huaiqinwu exponentialstabilityofstochasticdelayedneuralnetworkswithinverseholderactivationfunctionsandmarkovianjumpparameters |