Dong Tao, Song Yadi, Li Huaqing, Wang Xin, Huang Tingwen
IEEE Trans Neural Netw Learn Syst. 2025 Jul;36(7):12106-12116. doi: 10.1109/TNNLS.2024.3445116.
Phase-change memory (PCM) is a novel type of nonvolatile memory and is suitable for artificial neural synapses. This article investigates the Lagrange global exponential stability (LGES) of a class of PCNNs with mixed time delays. First, based on the conductivity characteristics of PCM, a piecewise equation is established to describe the electrical conductivity of PCM. By using the proposed piecewise equation to simulate the neural synapses, a novel PCNN with discrete and distributed time delays is proposed. Then, using comparative theory and fundamental inequalities, the LGES conditions based on the M-matrix are proposed in the sense of Filippov, and the exponential attractive set (EAS) is obtained based on M-matrix and external input. Moreover, the Lyapunov global exponential stability (GES) conditions of PCNNs without external input are obtained by using the inequality technique and eigenvalue theory, which is a form of M-matrix. Finally, two simulation examples are given to verify the validity of the obtained results.
相变存储器（PCM）是一种新型非易失性存储器，适用于人工神经突触。本文研究了一类具有混合时滞的脉冲耦合神经网络（PCNN）的拉格朗日全局指数稳定性（LGES）。首先，基于PCM的电导率特性，建立了一个分段方程来描述PCM的电导率。通过使用所提出的分段方程来模拟神经突触，提出了一种具有离散和分布时滞的新型PCNN。然后，利用比较理论和基本不等式，在菲利波夫意义下提出了基于M矩阵的LGES条件，并基于M矩阵和外部输入得到了指数吸引集（EAS）。此外，利用不等式技术和特征值理论得到了无外部输入的PCNN的李雅普诺夫全局指数稳定性（GES）条件，其为M矩阵的一种形式。最后，给出了两个仿真例子来验证所获结果的有效性。
