Stability Of Memristor-based Synchronous Switching Neural Networks With Time Delays

With the rapid development of artificial intelligence, artificial neural network has been widely researched since the 1940 s. In recent years, with the constantly emerging material objects of nanoscale memristors and the more in-deepth research of the theory of memristors, neural networks which use memristors as synaptic junctions have been become the research hot spot in the field of neuromorphic engineering. On the basis of existing researches, this paper put forward two kinds of new-type memristor-based neural network models and analyzed the stability of these two models respectively.Some global exponential stability conditions of these two kinds of systems were obtained, and the effectiveness of the conclusions were verified by numerical simulations. Specifically, the main research results in this paper were shown below:1.On the basis of the existing memristor-based neural network models, by introducing time-delay activation functions, we established a kind of memristor-based neural networks with time-varying delays and studied the global exponential stability conditions of the memristor-based neural network which is under the condition of time-varying delays. We got an exponential stability condition which relies on the time delays of the system by using Lyapunov-Krsasovskii stability theories and some inequality techniques, this condition canceled the limits of binary numerical connection weights of memristors. MATLAB numerical simulation verified the correctness of the theoretical results.2.On the basis of the above memristor-based neural network model, combining the ideas of switching, we considered the memristor-based neural networks whoseparameters depending on the state as independent subsystems of a switching system.Besides, we assumed that the controller of system is fully synchronous with the switching of subsystems. Then, we established a kind of memristor-based synchronous switching neural networks with time delays. We analyzed the global exponential stability of this model by using Lyapunov-Krsasovskii stability theory and some inequality techniques. The rules of the stability revealed that the convergence rate of the system depended on the time delays and the dwell time of switching. Numerical simulations on MATLAB verified the correctness of the theoretical results.