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A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks
Abstract
In this paper, we derive a new fixed-time stability theorem based on definite integral, variable substitution and some inequality techniques. The fixed-time stability criterion and the upper bound estimate formula for the settling time are different from those in the existing fixed-time stability theorems. Based on the new fixed-time stability theorem, the fixed-time synchronization of neural networks is investigated by designing feedback controller, and sufficient conditions are derived to guarantee the fixed-time synchronization of neural networks. To show the usability and superiority of the obtained theoretical results, we propose a secure communication scheme based on the fixed-time synchronization of neural networks. Numerical simulations illustrate that the new upper bound estimate formula for the settling time is much tighter than those in the existing fixed-time stability theorems. Moreover, the plaintext signals can be recovered according to the new fixed-time stability theorem, while the plaintext signals cannot be recovered according to the existing fixed-time stability theorems.
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Cites
Neural networks and physical systems with emergent collective computational abilities.
Hopfield, J. J. (1982) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.79.8.2554 · Cited by 19,270
Hopfield, J. J. (1984) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.81.10.3088 · Cited by 6,918
Cited by
Qi, X., Xu, S., & Liu, W. (2025) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2025.3582854 · Cited by 7
Jiao, J., Li, J., Chen, J., & Zhang, R. (2026) · Asian Journal of Control · doi:10.1002/asjc.3705 · Cited by 2
Metadata
- Authors
- Chen, C., Li, L., Peng, H., Yang, Y., Mi, L., & Zhao, H.
- Venue
- Neural Networks
- Publisher
- Elsevier BV
- Published
- 2020-03
- Volume
- 123
- Pages
- 412-419
- ISSN
- 0893-6080 (ISSN-L)
- OpenAlex
- W3000689905
- Cited by
- 275
- References
- 2
- FWCI
- 16.15
- Type
- journal article
- Language
- en
- Open access
- closed
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