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Updated: Dec 30, 2025

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
Published on: May 25, 2019
A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks
Chuan Chen1, Lixiang Li2, Haipeng Peng2
1School of Cyber Security, Qilu University of Technology, Jinan 250353, China; Shandong Provincial Key Laboratory of Computer Networks, Jinan, 250353, China.
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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