New Criteria on Stability of Dynamic Memristor Delayed Cellular Neural Networks

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(n) equilibrium points (EPs) and 2(n) 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.

Automated summary

Dynamic memristor-cellular neural networks replace linear resistors with flux-controlled memristors in each cell, providing the advantage of disappearing voltages, currents, and power consumption when reaching a steady state. Previous studies on stability rarely considered time delay, which has a significant impact on system stability. By extending the original system to a DM-D(delay)CNNs model and using Lyapunov method and matrix theory, new sufficient conditions for global asymptotic and exponential stability of DM-DCNNs with a known convergence rate are obtained. The results show the potential applications and advantages of DM-DCNNs in various fields.