Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances
This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method,...
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| Format: | Article |
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MDPI AG
2024-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/6/917 |
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| author | Jibin Yang Xiaohui Xu Quan Xu Haolin Yang Mengge Yu |
| author_facet | Jibin Yang Xiaohui Xu Quan Xu Haolin Yang Mengge Yu |
| author_sort | Jibin Yang |
| collection | DOAJ |
| description | This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method, some criteria are provided for securing the mean-square exponential stability of the mixed-delay QVNNs under impulsive and stochastic disturbances. Furthermore, a type of chaotic QVNNs under stochastic and impulsive disturbances is considered using a previously established stability analysis method. After the completion of designing the linear feedback control law, some sufficient conditions are obtained using the vector Lyapunov function method for determining the mean-square exponential synchronization of drive–response systems. Finally, two examples are provided to demonstrate the correctness and feasibility of the main findings and one example is provided to validate the use of QVNNs for image associative memory. |
| first_indexed | 2024-04-24T18:02:51Z |
| format | Article |
| id | doaj.art-9f911d54f99248a49af438aa0e7330a7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-24T18:02:51Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9f911d54f99248a49af438aa0e7330a72024-03-27T13:53:18ZengMDPI AGMathematics2227-73902024-03-0112691710.3390/math12060917Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-DisturbancesJibin Yang0Xiaohui Xu1Quan Xu2Haolin Yang3Mengge Yu4Vehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Xihua University, Chengdu 610039, ChinaVehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Xihua University, Chengdu 610039, ChinaSchool of Mechanical Engineering, Xihua University, Chengdu 610039, ChinaVehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Xihua University, Chengdu 610039, ChinaCollege of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, ChinaThis paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method, some criteria are provided for securing the mean-square exponential stability of the mixed-delay QVNNs under impulsive and stochastic disturbances. Furthermore, a type of chaotic QVNNs under stochastic and impulsive disturbances is considered using a previously established stability analysis method. After the completion of designing the linear feedback control law, some sufficient conditions are obtained using the vector Lyapunov function method for determining the mean-square exponential synchronization of drive–response systems. Finally, two examples are provided to demonstrate the correctness and feasibility of the main findings and one example is provided to validate the use of QVNNs for image associative memory.https://www.mdpi.com/2227-7390/12/6/917quaternion-valued neural networksimpulsive disturbancesstochastic disturbancesmixed delaysmean-square exponential stabilitymean-square exponential synchronization |
| spellingShingle | Jibin Yang Xiaohui Xu Quan Xu Haolin Yang Mengge Yu Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances Mathematics quaternion-valued neural networks impulsive disturbances stochastic disturbances mixed delays mean-square exponential stability mean-square exponential synchronization |
| title | Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances |
| title_full | Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances |
| title_fullStr | Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances |
| title_full_unstemmed | Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances |
| title_short | Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances |
| title_sort | stability and synchronization of delayed quaternion valued neural networks under multi disturbances |
| topic | quaternion-valued neural networks impulsive disturbances stochastic disturbances mixed delays mean-square exponential stability mean-square exponential synchronization |
| url | https://www.mdpi.com/2227-7390/12/6/917 |
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