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

Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this paper, the problem of stability analysis for a class of impulsive stochastic Cohen–Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen–Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.This work was supported by the Natural Science Foundation of CQ CSTC under grant 2007BB0430, the Scientific Research Fund of Chongqing Municipal Education Commission under Grant KJ070401, an International Joint Project sponsored by the Royal Society of the UK and the National Natural Science Foundation of China, and the Alexander von Humboldt Foundation of Germany

Recent Advances and Applications of Fractional-Order Neural Networks

This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed

Asymptotic Stability and Exponential Stability of Impulsive Delayed Hopfield Neural Networks

A criterion for the uniform asymptotic stability of the equilibrium point of impulsive delayed Hopfield neural networks is presented by using Lyapunov functions and linear matrix inequality approach. The criterion is a less restrictive version of a recent result. By means of constructing the extended impulsive Halanay inequality, we also analyze the exponential stability of impulsive delayed Hopfield neural networks. Some new sufficient conditions ensuring exponential stability of the equilibrium point of impulsive delayed Hopfield neural networks are obtained. An example showing the effectiveness of the present criterion is given

Finite-time Anti-synchronization of Memristive Stochastic BAM Neural Networks with Probabilistic Time-varying Delays

This paper investigates the drive-response finite-time anti-synchronization for memristive bidirectional associative memory neural networks (MBAMNNs). Firstly, a class of MBAMNNs with mixed probabilistic time-varying delays and stochastic perturbations is first formulated and analyzed in this paper. Secondly, an nonlinear control law is constructed and utilized to guarantee drive-response finite-time anti-synchronization of the neural networks. Thirdly, by employing some inequality technique and constructing an appropriate Lyapunov function, some anti-synchronization criteria are derived. Finally, a number simulation is provided to demonstrate the effectiveness of the proposed mechanism

New Results for Periodic Solution of High-Order BAM Neural Networks with Continuously Distributed Delays and Impulses

By M-matrix theory, inequality techniques, and Lyapunov functional method, certain sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential stability of periodic solution for a new type of high-order BAM neural networks with continuously distributed delays and impulses. These novel conditions extend and improve some previously known results in the literature. Finally, an illustrative example and its numerical simulation are given to show the feasibility and correctness of the derived criteria