IEEE Trans Cybern. 2022 Jun;52(6):5367-5379. doi: 10.1109/TCYB.2020.3031309. Epub 2022 Jun 16.
Dynamic memristor (DM)-cellular neural networks (CNNs), which replace a linear resistor with flux-controlled memristor in the architecture of each cell of traditional CNNs, have attracted researchers' attention. Compared with common neural networks, the DM-CNNs have an outstanding merit: when a steady state is reached, all voltages, currents, and power consumption of DM-CNNs disappeared, in the meantime, the memristor can store the computation results by serving as nonvolatile memories. The previous study on stability of DM-CNNs rarely considered time delay, while delay is quite common and highly impacts the stability of the system. Thus, taking the time delay effect into consideration, we extend the original system to DM-D(delay)CNNs model. By using the Lyapunov method and the matrix theory, some new sufficient conditions for the global asymptotic stability and global exponential stability with a known convergence rate of DM-DCNNs are obtained. These criteria generalized some known conclusions and are easily verified. Moreover, we find DM-DCNNs have 3 equilibrium points (EPs) and 2 of them are locally asymptotically stable. These results are obtained via a given constitutive relation of memristor and the appropriate division of state space. Combine with these theoretical results, the applications of DM-DCNNs can be extended to other fields, such as associative memory, and its advantage can be used in a better way. Finally, numerical simulations are offered to illustrate the effectiveness of our theoretical results.
动态忆阻器 (DM)-细胞神经网络 (CNN)，在传统 CNN 每个单元的结构中用磁通控制忆阻器代替线性电阻器，引起了研究人员的关注。与常见的神经网络相比，DM-CNN 具有突出的优点：当达到稳定状态时，所有电压、电流和 DM-CNN 的功耗都消失了，同时，忆阻器可以通过作为非易失性存储器来存储计算结果。以前关于 DM-CNN 稳定性的研究很少考虑时滞，而时滞是很常见的，会对系统的稳定性产生很大的影响。因此，考虑到时滞效应，我们将原始系统扩展到 DM-D(delay)CNN 模型。通过使用 Lyapunov 方法和矩阵理论，得到了 DM-DCNNs 全局渐近稳定和全局指数稳定的一些新的充分条件，且具有已知的收敛速度。这些准则推广了一些已知的结论，并且易于验证。此外，我们发现 DM-DCNNs 有 3 个平衡点 (EPs)，其中 2 个是局部渐近稳定的。这些结果是通过给定的忆阻器本构关系和状态空间的适当划分得到的。结合这些理论结果，可以将 DM-DCNNs 的应用扩展到其他领域，如联想记忆等，并且可以更好地利用其优势。最后，通过数值模拟验证了我们理论结果的有效性。
