Memristive Neural Networks Research Articles

Quasi‐stabilization/synchronization of quaternion‐valued memristive neural networks: Norm approach

This paper examines the quasi‐stabilization and synchronization of memristive neural networks in high dimensional forms. First, new criteria for the existence of the equilibrium point (EP) are delivered by contraction mapping principle. Then, a new Lyapunov function described with one‐norm form is imported for quasi‐stabilization/synchronization of the system. Finally, two numerical examples containing simulations are given to demonstrate the effectiveness.

Dynamics in a memristive neural network with three discrete heterogeneous neurons and its application

Dynamics in a memristive neural network with three discrete heterogeneous neurons and its application

Finite-Time Synchronization Criteria for Caputo Fractional-Order Uncertain Memristive Neural Networks with Fuzzy Operators and Transmission Delay Under Communication Feedback

Unlike existing memristive neural networks or fuzzy neural networks, this article investigates a class of Caputo fractional-order uncertain memristive neural networks (CFUMNNs) with fuzzy operators and transmission delay to realistically model complex environments. Especially, the fuzzy symbol AND and the fuzzy symbol OR as well as nonlinear activation behaviors are all concerned in the generalized master-slave networks. Based on the characteristics of the neural networks being studied, we have designed distinctive information feedback control protocols including three different functional sub-modules. Combining comparative theorems, inequality techniques, and stability theory, novel delay-independent conditions can be derived to ensure the finite-time synchronization (FTS) of fuzzy CFUMNNs. Besides, the upper bound of the settling time can be effectively evaluated based on feedback coefficients and control parameters, which makes the achievements of this study more practical for engineering applications such as signal encryption and secure communications. Ultimately, simulation experiments show the feasibility of the derived results.

Three-Dimensional Space Chaotic Scrolls Generated by Memristive Hopfield Neural Network and Its Application in Robot Path Planning

Abstract In this paper, a novel three-dimensional space-scroll chaotic attractor is constructed by introducing piece-wise linear memristors into a three-neurons-based Hopfield neural network to simulate the electromagnetic influence on neural dynamics. The dynamical behaviors of the novel memristive Hopfield neural network are discussed by means of numerical methods including the Lyapunov exponent spectrum, bifurcation diagrams, phase plots and dynamic maps. Furthermore, we also investigated different neurons subject to the memristive electromagnetic influence, where the two-dimensional grid-scroll chaotic attractors can be generated by one neuron subjects to the electromagnetic influence and three-dimensional space-scroll chaotic attractors can be generated by all of the neurons subject to the memristive electromagnetic influence. Moreover, we present a three-dimensional space-scroll scroll attractor-based chaotic mobile robot system. Superiority of the proposed space-scroll-based chaotic mobile robot system compared to existing methods has been demonstrated through numerical simulations.

Firing Analysis of a Memristive Synapse-Coupled Heterogeneous Neural Network with Activation Gradient

Firing Analysis of a Memristive Synapse-Coupled Heterogeneous Neural Network with Activation Gradient

Regulation and analysis of multi-scroll attractors in a class of memristive Hopfield neural networks with high Lyapunov exponents

Multi-scroll chaotic systems have gained significant attention in recent years. However, there is little research on the chaotic systems of memristive neural networks with multiple complex structural attractors. A class of multi-scroll chaotic systems are designed in this paper, which are based on Hopfield neural network by using memristors as synapses. Implementing synaptic control with memristors at various coupling positions allows for the creation of multiple chaotic attractors with distinct topological structures. The proposed systems exhibit special and irregular shaped attractors, and can generate a fixed number of scrolls. Through analysis we find that the systems have high Lyapunov exponents, indicating strong sensitivity and randomness. Meanwhile, the systems exhibit extremely rich dynamic behaviors, such as symmetric coexistence phenomena. Especially, we observe signal amplitude control and offset boosting phenomena in the systems. In addition, simulation circuits are designed based on such chaotic systems to verify the physical feasibility of the systems.

Event-based nonfragile state estimation for memristive neural networks with multiple time-delays and sensor saturations

This article investigates the issue of nonfragile state estimation (SE) for memristor-based neural networks (MNNs) with leakage delay and proportional delay. In actual engineering, a multitude of usefulness data are transmitted to the estimator through the networks, which stress the burden on communication bandwidth. A dynamic event-triggered mechanism (DETM) that relies on incomplete measurements is utilised to select valuable data. A novel delay-dependent criterion for the existence of the event-based state estimator is derived in terms of a convex optimisation problem by means of the Lyapunov theory and some integer inequalities technique. In the end, two numerical simulations are shown to illustrate the validity of the proposed theoretical methods.

State Estimation for Measurement-Saturated Memristive Neural Networks with Missing Measurements and Mixed Time Delays Subject to Cyber-Attacks: A Non-Fragile Set-Membership Filtering Framework

This paper is concerned with the state estimation problem based on non-fragile set-membership filtering for a class of measurement-saturated memristive neural networks (MNNs) with unknown but bounded (UBB) noises, mixed time delays and missing measurements (MMs), subject to cyber-attacks under the framework of weighted try-once-discard protocol (WTOD protocol). Considering bandwidth-limited open networks, this paper proposes an improved set-membership filtering based on WTOD protocol to partially solve the problem that multiple sensor-related problems and multiple network-induced phenomena influence the state estimation performance of MNNs. Moreover, this paper also discusses the gain perturbations of the estimator and proposes an improved non-fragile estimation framework based on set-membership filtering, which enhances the robustness of the estimation approach. The proposed estimation framework can effectively estimate the state of MNNs with UBB noises, estimator gain perturbations, mixed time-delays, cyber-attacks, measurement saturations and MMs. This paper first utilizes mathematical induction to provide the sufficient conditions for the existence of the desired estimator, and obtains the estimator gain by solving a set of linear matrix inequalities. Then, a recursive optimization algorithm is utilized to achieve optimal estimation performance. The effectiveness of the theoretical results is verified by comparative numerical simulation examples.

Exponential Synchronization Control of Reaction-Diffusion Fuzzy Memristive Neural Networks: Hardy-Poincarè Inequality.

This article is devoted to solving the exponential synchronization problem of a new type of fuzzy memristive neural network with reaction-diffusion terms. By introducing adaptive laws, two controllers are designed. After combining the inequality technique with the Lyapunov function approach, some easily verified sufficient conditions are established to ensure the exponential synchronization of the reaction-diffusion fuzzy memristive system under the proposed adaptive scheme. In addition, by using the Hardy-Poincarè inequality, the diffusion terms are estimated associated with the information of the reaction-diffusion coefficients and the regional feature, which improves some existing conclusions. Finally, an illustrative example is presented to demonstrate the validity of the theoretical results.

Robust Design of Two-Level Non-Integer SMC Based on Deep Soft Actor-Critic for Synchronization of Chaotic Fractional Order Memristive Neural Networks

Robust Design of Two-Level Non-Integer SMC Based on Deep Soft Actor-Critic for Synchronization of Chaotic Fractional Order Memristive Neural Networks

Concise Exponential Stability Conditions for BAM Quaternion Memristive Neural Networks Affected by Mixed Delays

Concise Exponential Stability Conditions for BAM Quaternion Memristive Neural Networks Affected by Mixed Delays

Grid Multibutterfly Memristive Neural Network With Three Memristive Systems: Modeling, Dynamic Analysis, and Application in Police IoT

Grid Multibutterfly Memristive Neural Network With Three Memristive Systems: Modeling, Dynamic Analysis, and Application in Police IoT

Dynamics analysis and FPGA implementation of discrete memristive cellular neural network with heterogeneous activation functions

The activation function, as an important component of artificial neural networks, endows neural networks with rich dynamical phenomena by virtue of its nonlinear properties. However, especially for cellular neural networks (CNNs), the exploration of neural networks consisting of heterogeneous activation functions has not been sufficient. In this article, we introduce heterogeneous activation functions in discrete cellular neural network (DCNN) for the first time. In order to enhance the dynamics of the original DCNN, we propose our discrete memristive cellular neural network (DMCNN) based on a memristor with a sinusoidal function. Using various methods of dynamical characterization, such as Lyapunov exponential analysis, bifurcation diagrams and spectral entropy, the rich dynamical behaviour of the proposed model is comprehensively investigated, including hyperchaos, transient chaos, high spectral entropy and multiple types of coexisting attractors in the proposed model. Last but not least, the hardware platform of the proposed model is implemented by field programmable gate array (FPGA), and the dynamics of the proposed model is verified by a combination of software simulation and hardware experiments. The new exploration of DMCNN with heterogeneous activation functions in this article lays the foundation for further research into neural networks with complex dynamical behaviour.

Finite-time synchronization of proportional delay memristive competitive neural networks

The finite-time synchronization (FTS) is considered for proportional delay memristive competitive neural networks (PDMCNNs). By utilizing Lyapunov functional method and differential inclusion theory, two new criteria ensuring the FTS of PDMCNNs are established. These criteria with algebraic inequality forms are less complicated and easier to verify than the matrix inequality forms. In addition, the corresponding settling times have been estimated. Eventually, the effectiveness of the presented criteria and controllers is confirmed through two numerical examples, and one application about image encryption is provided.

Fault-Tolerant Synchronization for Memristive Neural Networks With Multiple Actuator Failures.

By using the fault-tolerant control method, the synchronization of memristive neural networks (MNNs) subjected to multiple actuator failures is investigated in this article. The considered actuator failures include the effectiveness failure and the lock-in-place failure, which are different from previous results. First of all, the mathematical expression of the control inputs in the considered system is given by introducing the models of the above two types of actuator failures. Following, two classes of synchronization strategies, which are state feedback control strategies and event-triggered control strategies, are proposed by using some inequality techniques and Lyapunov stability theories. The designed controllers can, respectively, guarantee the realization of synchronizations of the global exponential, the finite-time and the fixed-time for the MNNs by selecting different parameter conditions. Then the estimations of settling times of provided synchronization schemes are computed and the Zeno phenomenon of proposed event-triggered strategies is explicitly excluded. Finally, two experiments are conducted to confirm the availability of given synchronization strategies.

Synchronization for Delayed Fractional-Order Memristive Neural Networks Based on Intermittent-Hold Control with Application in Secure Communication

Synchronization for Delayed Fractional-Order Memristive Neural Networks Based on Intermittent-Hold Control with Application in Secure Communication

Non-fragile output-feedback control for delayed memristive bidirectional associative memory neural networks against actuator failure

This article investigates the stabilization property for the modeled memristive bidirectional associative memory neural networks with time-varying delay when the faulty signals received from the fluctuated controller. The non-fragile output-feedback controller is taken into account to counteract the impact of gain perturbations to end up with robust fault-tolerant setup. To tackle the weak signals in the actuator received from the fluctuated controller, control gain matrices encompass situations intended to memory non-fragile output-feedback controller. Based on the Lyapunov stability theory, differential inclusion theory, and congruence transformation, the sufficient condition for the global asymptotic stabilization property for the designed fault-tolerant memristive bidirectional associative memory neural network model is obtained in terms of linear matrix inequality by utilizing Wirtinger's inequality. Finally, numerical examples are approached with the state performance plots of the proposed memristive bidirectional associative memory neural network model with respect to the time-domain plane, to confirm the stabilization results and it illustrates the working mechanism of the designed controller.

General decay anti-synchronization and [formula omitted] anti-synchronization of derivative coupled delayed memristive neural networks with constant and delayed state coupling

In this article, we explore the general decay anti-synchronization (GDAS) and general decay H∞ anti-synchronization (GDHAS) of derivative coupled delayed memristive neural networks (DCDMNNs) with constant and delayed state coupling, respectively. To begin with, on account of the definitions of ψ-type function as well as ψ-type stability, we present the GDAS and GDHAS concepts for the considered DCDMNNs. What is more, several sufficient conditions are derived for reaching GDAS and GDHAS of DCDMNNs with constant and delayed state coupling by selecting correct Lyapunov functionals and devising a proper controller. Moreover, numerical simulations examples are provided to demonstrate the feasibility of the obtained conclusions.

Fixed-time synchronization of interconnected memristive neural networks with energy consumption via switched control

The fixed-time synchronization of time-delay interconnected memristive neural networks is probed in this article. Firstly, according to the conventional controller, a new type of switching controller is proposed, which can complement each other. By utilizing the theory of Lyapunov stability and differential inclusion, it is proved that interconnected memristive neural networks can achieve synchronization within a fixed time under the designed controller. In addition, to control engineering costs, the upper limit of energy consumption, which is produced by the controller from the initial time to the settling-time, is estimated. Finally, numerical examples are provided to verify the validity of the theoretical results.

Finite-time stability of fractional-order quaternion-valued memristive neural networks with time delay

This study addresses the finite-time stability (FTS) problem of fractional-order quaternion-valued memristive neural networks (FQMNNs) with time delay. Firstly, by leveraging set-valued mapping, differential inclusion, and contracting mapping principle, the sufficient condition is provided to assure the existence and uniqueness of the equilibrium point. Secondly, given the fractional order differential inequality and Gronwall inequality, a finite-time stability (FTS) criterion is obtained for the delayed FQMNNs with the fractional order between 0 and 1. Additionally, a sufficient condition is proposed to guarantee the FTS of FQMNNs with the fractional order between 1 and 2. Compared with existing results, this study not only extends the fractional order between 0 and 2, but also incorporates quaternions, which significantly enhances the FTS theory. Finally, two numerical examples demonstrate the practicality of the obtained results.