Class Of Memristive Neural Networks Research Articles

Simple cyclic memristive neural networks with coexisting attractors and large-scale amplitude control.

The memristor's unique memory function and non-volatile nature make it an ideal electronic bionic device for artificial neural synapses. This paper aims to construct a class of memristive neural networks (MNNs) with a simple circular connection relationship and complex dynamics by introducing a generic memristor as synapse. For placing the memristive synapse in different coupling positions, three MNNs with the same coupling cyclic connection are yielded. One remarkable feature of the proposed MNNs is that they can yield complex dynamics, in particular, abundant coexisting attractors and large-scale parameter-relied amplitude control, by comparing with some existing MNNs. Taking one of the MNNs as an example, the complex dynamics (including chaos, period-doubling bifurcation, symmetric coexisting attractors, large-scale amplitude control) and circuit implementation are studied . The number of equilibria and their stabilities are discussed. The parameter-relied dynamic evolution and the coexisting attractors are numerically shown by using bifurcations and phase portraits. A microcontroller-based hardware circuit is given to realize the network, which verifies the correctness of the numerical results and experimental results.

Discontinuous Event-Triggered Control for Local Stabilization of Memristive Neural Networks With Actuator Saturation: Discrete- and Continuous-Time Lyapunov Methods.

In this article, the local stabilization problem is investigated for a class of memristive neural networks (MNNs) with communication bandwidth constraints and actuator saturation. To overcome these challenges, a discontinuous event-trigger (DET) scheme, consisting of the rest interval and work interval, is proposed to cut down the triggering times and save the limited communication resources. Then, a novel relaxed piecewise functional is constructed for closed-loop MNNs. The main advantage of the designed functional consists in that it is positive definite only in the work intervals and the sampling instants but not necessarily inside the rest intervals. With the aid of extended reciprocally convex combination lemma, generalized sector condition, and some inequality techniques, two local stabilization criteria are established on the basis of both the discrete- and continuous-time Lyapunov methods. The proposed analysis technique fully takes advantage of the looped-functional and the event-trigger mechanism. Moreover, two optimization schemes are, respectively, established to design the control gain and enlarge the estimates of the admissible initial conditions (AICs) and the upper bound of rest intervals. Finally, some comparison results are given to validate the superiority of the proposed method.

Finite/fixed-time synchronization of memristive neural networks via event-triggered control

By applying event-triggered control schemes, this paper investigates the issues of finite/fixed-time synchronization for a class of memristive neural networks (MNNs). In order to reduce the transmission burden and realize a fast rate of synchronization, the appropriate controller and the measurement error function are designed. Then, by using Lyapunov stability theory and inequality techniques, some efficient criteria are proposed to guarantee the finite/fixed-time synchronization, respectively. Besides, the estimations of the synchronization time are derived, and the Zeno phenomenon can be excluded under the derived event-triggered schemes. Finally, simulations are provided to verify the obtained results.

Fixed-Time Synchronization of Delayed Memristive Neural Networks with Discontinuous Activations

In this paper, the fixed-time synchronization problem for a class of memristive neural networks with discontinuous neuron activation functions and mixed time-varying delays is investigated. With the help of the fixed-time stability theory, under the framework of Filippov solution and differential inclusion theory, several new and useful sufficient criteria for fixed-time synchronization are obtained by designing two types of energy-saving and simple controllers for the considered systems. Compared with the traditional fixed-time synchronization controller, the controllers used in this paper only have one power exponent term, which is a function of the system state error rather than a constant. Moreover, some previous relevant works are especially improved. Finally, two numerical examples are given to show the correctness and the effectiveness of the obtained theoretical results.

Exponential and fixed‐time stabilization of memristive neural networks with mixed delays

In this paper, we study a class of memristive neural networks with mixed delays. The existence of its equilibrium point is proved without the boundedness and initial value of the activation function, and a criterion to ensure its exponential stabilization under a sampled‐data controller is obtained by constructing an appropriate Lyapunov function. Meanwhile, the fixed‐time stabilization of memristive neural networks is also proved by the Lyapunov method. The obtained results extend and enhance some existing ones, and are illustrated by numerical examples.

Sliding Mode Stabilization of Memristive Neural Networks With Leakage Delays and Control Disturbance.

In this article, we investigate a class of memristive neural networks (MNNs) with time-varying delays and leakage delays via sliding mode control (SMC) with and without control disturbance. SMC is used to ensure MNNs' stability. According to the characteristics of the MNNs, we consider the following three models: the first is the MNNs with time-varying delays, the second is the MNNs with time-varying delays and the control disturbance, and the third is the MNNs with time-varying delays, leakage delays, and the control disturbance. We quote some assumptions and lemmas to ensure that our main results are true. The sliding surface, the corresponding sliding mode controller, and the Lyapunov functions are constructed in different models to ensure MNNs' stability. Finally, some examples and simulations verify the validity of our main results by solving linear matrix inequality (LMI), and the conclusions and analysis of the results are given.

Passivity and passification of quaternion‐valued memristive neural networks

In this paper, a class of memristive neural networks with quaternion‐valued connection weights is studied. By starting from some basic quaternion‐valued algorithms, the quaternion‐valued memristive system is obtained; then, some passivity criteria for the memristive neural networks are presented based on some appropriate auxiliary functions. Furthermore, to tackle with the passification problem, two kinds of control protocols are designed. What should be mentioned is that, in the above derived conclusions, the partial order is employed, which can be employed to compare the “magnitude” of two different quaternions, and thus, the closed convex hull consisted by quaternion can be derived correspondingly. In the end, the analytical design are substantiated with two numerical results.

Exponential stability for a class of memristive neural networks with mixed time-varying delays

A new general hybrid neural networks with inertial term and mixed time-varying delays are proposed here by using the memristors connections. Then by building appropriate Lyapunov functionals and inequality technique, some new conditions assuring the global exponential stability of the hybrid neural networks are derived. The circuit implementation of the proposed hybrid neural networks are also presented here. In addition, the new proposed results here enrich and extend the earlier publications on neural networks. Lastly, numerical simulations show the effectiveness of our results.

Global Uniform Asymptotic Fixed Deviation Stability and Stability for Delayed Fractional-order Memristive Neural Networks with Generic Memductance

In this paper, we study global uniform asymptotic fixed deviation stability and stability for a wide class of memristive neural networks with time-varying delays. Firstly, a new mathematical expression of the generic memductance (memristance) is proposed according to the feature of the memristor and the general current–voltage characteristic and a new class of neural networks is designed. Next, a new concept of stability (fixed deviation stability) is proposed in order to describe veritably the stability characteristics of the discontinuous system and the sufficient conditions are given to guarantee the global uniform asymptotic fixed deviation stability and stability of the new system. Finally, two numerical examples are provided to show the applicability and effectiveness of our main results.

Exponential stabilisation of stochastic memristive neural networks under intermittent adaptive control

This study focuses on the exponential stabilisation problem for a general class of memristive neural networks subjected to both stochastic disturbance and time-varying delays under periodically intermittent adaptive control. The stochastic disturbances are described as Brownian motions in the considered networks. An adaptive updated rule and a periodically intermittent adaptive control strategy are designed for the exponential stabilisation of memristive neural networks subjected to both stochastic disturbance and time-varying delays. Then, by adopting the adaptive control technique, differential inclusion theory and set-valued maps, and by building a new Lyapunov–Krasovskii functional, many novel sufficient conditions are proposed to guarantee exponential stabilisation for stochastic memristive neural networks. Different from existing results on stabilisation of stochastic memristive neural networks, the obtained criteria in this study are directly derived according to the parameters of networks. Finally, an example is carried out to demonstrate the validity of the theoretic results.

Passivity analysis of memristive neural networks with mixed time-varying delays and different state-dependent memductance functions

This paper is concerned with the problem of passivity analysis for a class of memristive neural networks with mixed time-varying delays and different state-dependent memductance functions. By employing the theories of differential inclusions and set-valued maps, delay-dependent criteria in terms of linear matrix inequalities are obtained for the passivity of the memristive neural networks. Finally, numerical examples are given to illustrate the feasibility of the theoretical results.

Coexistence and local [formula omitted]-stability of multiple equilibrium points for memristive neural networks with nonmonotonic piecewise linear activation functions and unbounded time-varying delays

In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n-neuron MNNs can have 5n equilibrium points located in ℜn, and 3n of them are locally μ-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log–log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results.

Adaptive exponential synchronization of memristive neural networks with mixed time-varying delays

This study is focused on the issue of adaptive exponential synchronization for a general class of memristive neural networks (MNNs) with mixed time-varying delays. A new and simple adaptive controller with feedback control law is designed to achieve exponential synchronization by using Lyapunov functional method. The adaptive controller proposed in the paper possesses a powerful adaptive capability that it can be utilized for various MNNs with different mathematical definitions of memristor. In addition, no excessive calculations such as solving linear matrix inequality or computing algebraic conditions are required in our synchronization criteria. We also present two synchronization conditions for a special class of MNNs that part or even all of the system׳s right-hand is reduced to be continuous when activation functions are zero at the neuron׳s switching points. And two lemmas are introduced to modify a misunderstanding in this situation in some previous papers. Finally, an example with numerical simulations is presented to illustrate the efficiency and accuracy of the theoretical results.

Passivity analysis of memristive neural networks with probabilistic time-varying delays

The passivity problem has been further researched for a class of memristive neural networks with probabilistic time-varying delays in this paper. Based on an effective Lyapunov functional and the Wirtinger-type inequality, sufficient conditions are presented to guarantee the passive performance of the memristive models. By establishing a stochastic variable with Bernoulli distribution, the information of probabilistic time-varying delays are considered, which were transformed into one with deterministic time-varying delay and stochastic parameters. Moreover, the range of the delays as well as the probability distribution of its variation are all taken into consideration, thus, the results derived in this paper are more reasonable. Finally, the advantages of the proposed techniques are demonstrated by two numerical examples.

New algebraic conditions for ISS of memristive neural networks with variable delays

In this paper, a general class of memristive neural networks with variable delays is studied. By utilizing control theory and nonsmoooth analysis, two sufficient criteria ensuring input-to-state stability of memristive neural networks with variable delays are firstly obtained which are novel and more practical than the previous works in the literature. Finally, a numerical example is given to demonstrate the effectiveness of our results.

Combined H∞ and passivity state estimation of memristive neural networks with random gain fluctuations

In this paper, we discussed non-fragile state estimation problem for a class of memristive neural networks with two different types of memductance functions and uncertain time-varying delays. The required results are derived by using a suitable Lyapunov–Krasovskii functional (LKF) and using linear matrix inequality (LMI) approach together with Wirtinger-type inequality analysis. The sufficient conditions are presented for the existence of non-fragile state estimator based on the combined H∞ and passivity performance criterions. The results are proposed in terms of LMIs, which can guarantee the global asymptotic stability of the error dynamics between the considered memristive RNNs and its non-fragile observer. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results via simulations.

Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays

As an indispensable part of memristive synaptic weights, the switching jumps can induce instability, oscillation or even chaos to the memristive network system. Based on the available information of the switching jumps, this paper is concerned with the stochastic exponential synchronization of a class of memristive neural networks with multiple time-varying delays. By using stochastic differential inclusions and Lyapunov stability theory, discontinuous state feedback controller which depends upon the switching jumps is proposed. Compared with the previous state feedback scheme, more information of memristive synaptic weights is used to design the synchronous controller which ensures the stochastic exponential synchronization of considered networks. When the information of switching jumps is incomplete, discontinuous adaptive controller which is independent of the switching jumps is also designed, thus the applicability of synchronization is broadened. A numerical example is provided to illustrate the effectiveness and potential of the proposed design techniques.

Input-to-State Stability of Stochastic Memristive Neural Networks with Time-Varying Delay

This paper is concerned with the input-to-state stability problem of a class of memristive neural networks. We consider the neural networks that take into account both the stochastic effects and time-varying delay, and introduce the notions of meansquare exponential input-to-state stability. Using the stochastic analysis theory and Itô formula for stochastic differential equations, we establish sufficient conditions for both mean-square exponential input-to-state stability and mean-square exponential stability. Numerical simulations are also provided to demonstrate the theoretical results.

Finite-Time Anti-synchronization Control of Memristive Neural Networks With Stochastic Perturbations

In this paper, finite-time anti-synchronization control of memristive neural networks with stochastic perturbations is studied. We investigate a class of memristive neural networks with two different types of memductance functions. The purpose of the addressed problem is to design a nonlinear controller which can obtain anti-synchronization of the drive system and the response system in finite time. Based on two kinds of memductance functions, finite-time stability criteria are obtained for memristive neural networks with stochastic perturbations. The analysis in this paper employs differential inclusions theory, finite-time stability theorem, linear matrix inequalities and Lyapunov functional method. These theoretical analysis can characterize fundamental electrical properties of memristive systems and provide convenience for applications in pattern recognition, associative memories, associative learning, etc.. Finally, two numerical examples are given to show the effectiveness of our results.

Improved conditions for global exponential stability of a general class of memristive neural networks

Modeling and related characterization of memristive neurodynamic systems becomes a critical pathway towards neuromorphic system designs. This paper presents a general class of memristive neural networks with time-varying delays. Some improved algebraic criteria for global exponential stability of memristive neural networks are obtained. The criteria improve some previous results and are easy to be verified with the physical parameters of system itself. The proposed framework for theoretical analysis of memristive neurodynamic systems may be useful in developing nanoscale memristor device as synapse in neuromorphic computing architectures.