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

Weighted Sum Synchronization of Memristive Coupled Neural Networks

Funding Information: This work is supported by the National Natural Science Foundation of China (No. 61971185) and the Open Fund Project of Key Laboratory in Hunan Universities (No. 18K010). Publisher Copyright: © 2020 Elsevier B.V.It is well known that weighted sum of node states plays an essential role in function implementation of neural networks. Therefore, this paper proposes a new weighted sum synchronization model for memristive neural networks. Unlike the existing synchronization models of memristive neural networks which control each network node to reach synchronization, the proposed model treats the networks as dynamic entireties by weighted sum of node states and makes the entireties instead of each node reach expected synchronization. In this paper, weighted sum complete synchronization and quasi-synchronization are both investigated by designing feedback controller and aperiodically intermittent controller, respectively. Meanwhile, a flexible control scheme is designed for the proposed model by utilizing some switching parameters and can improve anti-interference ability of control system. By applying Lyapunov method and some differential inequalities, some effective criteria are derived to ensure the synchronizations of memristive neural networks. Moreover, the error level of the quasi-synchronization is given. Finally, numerical simulation examples are used to certify the effectiveness of the derived results.Peer reviewe

Finite time Synchronization of Inertial Memristive Neural Networks with Time Varying Delay

Finite time synchronization control of inertial memristor-based neural networks with varying delay is considered. In view of drive and response concept, the sufficient conditions to ensure finite time synchronization issue of inertial memristive neural networks is given. Based on Lyapunov finite time asymptotic theory, a kind of feedback controllers is designed for inertial memristorbased neural networks to realize the finite time synchronization. Based on Lyapunov stability theory, close loop error system can be proved finite time and fixed time stable. Finally, illustrative example is given to illustrate the effectiveness of theoretical results

Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument

We consider a new model for shunting inhibitory cellular neural networks, retarded functional differential equations with piecewise constant argument. The existence and exponential stability of almost periodic solutions are investigated. An illustrative example is provided.Comment: 24 pages, 1 figur

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

Electromagnetic Radiation Control for Nonlinear Dynamics of Hopfield Neural Networks

© 2024 Author(s). Published under an exclusive license by AIP Publishing. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1063/5.0194928Electromagnetic radiation (EMR) affects the dynamical behavior of the nervous system, and appropriate EMR helps to study the dynamic mechanism of the nervous system. This paper uses a sophisticated four-dimensional Hopfield neural network (HNN) model augmented with one or more memristors to simulate the effects of EMR. We focus on the chaotic dynamics of HNN under the influence of EMR. Complex dynamical behaviors are found and transient chaotic phenomena have the same initial value sensitivity, showing how transient chaos is affected by EMR. Multiperiodic phenomena induced by quasi-periodic alternations are found in the dual EMR, as well as the suppression properties of the dual EMR for system chaos. This implies that the dynamical behavior of the HNN system can be controlled by varying the amount of EMR or the number of affected neurons in the HNN. Finally, a strong validation of our proposed model is provided by Multisim and FPGA hardware.Peer reviewe

Synchronization of inertial memristive neural networks with time-varying delays via static or dynamic event-triggered control

Funding Information: This work was supported in part by the National Natural Science Foundation of China under Grant 61971185, the Major Research Project of the National Natural Science Foundation of China under Grant 91964108 and the Open Fund Project of Key Laboratory in Hunan Universities under Grant 18K010. Publisher Copyright: © 2020 Elsevier B.V.This paper investigates the synchronization problem of inertial memristive neural networks (IMNNs) with time-varying delays via event-triggered control (ETC) scheme and state feedback controller for the first time. First, two types of state feedback controllers are designed; the first type of controller is added to the transformational first-order system, and the second type of controller is added to the original second-order system. Next, based on each feedback controller, static event-triggered control (SETC) condition and dynamic event-triggered control (DETC) condition are presented to significantly reduce the update times of controller and decrease the computing cost. Then, some sufficient conditions are given such that synchronization of IMNNs with time-varying delays can be achieved under ETC schemes. Finally, a numerical simulation and some data analyses are given to verify the validity of the proposed results.Peer reviewe