Complete Stability of Neural Networks With Extended Memristors

Abstract

The article considers a large class of delayed neural networks (NNs) with extended memristors obeying the Stanford model. This is a widely used and popular model that accurately describes the switching dynamics of real nonvolatile memristor devices implemented in nanotechnology. The article studies via the Lyapunov method complete stability (CS), i.e., convergence of trajectories in the presence of multiple equilibrium points (EPs), for delayed NNs with Stanford memristors. The obtained conditions for CS are robust with respect to variations of the interconnections and they hold for any value of the concentrated delay. Moreover, they can be checked either numerically, via a linear matrix inequality (LMI), or analytically, via the concept of Lyapunov diagonally stable (LDS) matrices. The conditions ensure that at the end of the transient capacitor voltages and NN power vanish. In turn, this leads to advantages in terms of power consumption. This notwithstanding, the nonvolatile memristors can retain the result of computation in accordance with the in-memory computing principle. The results are verified and illustrated via numerical simulations. From a methodological viewpoint, the article faces new challenges to prove CS since due to the presence of nonvolatile memristors the NNs possess a continuum of nonisolated EPs. Also, for physical reasons, the memristor state variables are constrained to lie in some given intervals so that the dynamics of the NNs need to be modeled via a class of differential inclusions named differential variational inequalities.

A Memristor Neural Network Based on Simple Logarithmic-Sigmoidal Transfer Function with MOS Transistors

“…The analyses demonstrate a strong correlation between the obtained results, confirming the accurate functionality of the suggested memristor-based neural network. Memristor-based neural nets are more disposed to chaotic modes, owing to the highly nonlinear behavior of memristors and fluctuations of their parameters, and additional attention to ensure their stability is needed, especially when scaled up to a large number of nodes [38,39]. Additional simulations with different input signals were conducted and the results confirmed the proper operation of the considered…”

Artificial sensory system based on memristive devices

“…Depending on the degree of retainment of the resistance state, memristors are classified as volatile [37][38][39][40] and non-volatile memristors. [41][42][43][44] In the case of a volatile memristor, the resistance state temporarily changes from a high resistance state (HRS) to a low resistance state (LRS), when a voltage above a threshold value is applied. It recovers from the LRS to HRS after the removal of the applied voltage.…”