On the validity of memristor modeling in the neural network literature

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks

New results on finite-/fixed-time synchronization of delayed memristive neural networks with diffusion effects

In this paper, we further investigate the finite-/fixed-time synchronization (FFTS) problem for a class of delayed memristive reaction-diffusion neural networks (MRDNNs). By utilizing the state-feedback control techniques, and constructing a general Lyapunov functional, with the help of inequality techniques and the finite-time stability theory, novel criteria are established to realize the FFTS of the considered delayed MRDNNs, which generalize and complement previously known results. Finally, a numerical example is provided to support the obtained theoretical results

Almost Periodic Dynamics for Memristor-Based Shunting Inhibitory Cellular Neural Networks with Leakage Delays

We investigate a class of memristor-based shunting inhibitory cellular neural networks with leakage delays. By applying a new Lyapunov function method, we prove that the neural network which has a unique almost periodic solution is globally exponentially stable. Moreover, the theoretical findings of this paper on the almost periodic solution are applied to prove the existence and stability of periodic solution for memristor-based shunting inhibitory cellular neural networks with leakage delays and periodic coefficients. An example is given to illustrate the effectiveness of the theoretical results. The results obtained in this paper are completely new and complement the previously known studies of Wu (2011) and Chen and Cao (2002)