IEEE Trans Neural Netw Learn Syst. 2018 May;29(5):1822-1834. doi: 10.1109/TNNLS.2017.2688404. Epub 2017 Apr 12.
Recent papers in the literature introduced a class of neural networks (NNs) with memristors, named dynamic-memristor (DM) NNs, such that the analog processing takes place in the charge-flux domain, instead of the typical current-voltage domain as it happens for Hopfield NNs and standard cellular NNs. One key advantage is that, when a steady state is reached, all currents, voltages, and power of a DM-NN drop off, whereas the memristors act as nonvolatile memories that store the processing result. Previous work in the literature addressed multistability of DM-NNs, i.e., convergence of solutions in the presence of multiple asymptotically stable equilibrium points (EPs). The goal of this paper is to study a basically different dynamical property of DM-NNs, namely, to thoroughly investigate the fundamental issue of global asymptotic stability (GAS) of the unique EP of a DM-NN in the general case of nonsymmetric neuron interconnections. A basic result on GAS of DM-NNs is established using Lyapunov method and the concept of Lyapunov diagonally stable matrices. On this basis, some relevant classes of nonsymmetric DM-NNs enjoying the property of GAS are highlighted.
最近的文献介绍了一类具有忆阻器的神经网络（NN），称为动态忆阻器（DM）NN，使得模拟处理发生在电荷-通量域中，而不是像 Hopfield NN 和标准细胞 NN 那样发生在典型的电流-电压域中。一个关键优势是，当达到稳定状态时，DM-NN 的所有电流、电压和功率都会下降，而忆阻器则充当非易失性存储器，存储处理结果。文献中的先前工作解决了 DM-NN 的多稳定性问题，即在存在多个渐近稳定平衡点（EPs）的情况下，解的收敛性问题。本文的目的是研究 DM-NN 的一个基本不同的动态特性，即彻底研究 DM-NN 中唯一 EP 的全局渐近稳定性（GAS）的基本问题，这是在非对称神经元连接的一般情况下。使用 Lyapunov 方法和 Lyapunov 对角稳定矩阵的概念，建立了关于 DM-NN 的 GAS 的一个基本结果。在此基础上，突出了一些具有 GAS 性质的相关类非对称 DM-NN。
