Wu Xili, Tu Zhengwen, Peng Tao, Wang Dandan
School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China.
Sci Rep. 2024 Aug 2;14(1):17975. doi: 10.1038/s41598-024-68763-3.
This paper investigated the global attractive set for quaternion-valued neural networks (QVNNs) with leakage delay, time-varying delay, and neutral items. Based on various basic conditions of activation function, the global attractive set and global exponential attractive set of QVNNs are given combined with novel analytical techniques and Lyapunov theory. The QVNNs are studied by a direct method, without any decomposition. The time delay can be non-differential, which makes the results more pragmatic. Restrictions on the activation function of the neutral item are relaxed. The neutral activation function can be bounded or unbounded, which makes the results more practical. Two simulation examples are given to verify the validity of the theory results.
本文研究了具有泄漏延迟、时变延迟和中立项的四元数神经网络（QVNNs）的全局吸引集。基于激活函数的各种基本条件，结合新颖的分析技术和李雅普诺夫理论，给出了QVNNs的全局吸引集和全局指数吸引集。采用直接方法研究QVNNs，无需任何分解。时间延迟可以是不可微的，这使得结果更具实用性。放宽了对中立项激活函数的限制。中立激活函数可以是有界的或无界的，这使得结果更具实际意义。给出了两个仿真例子来验证理论结果的有效性。
