Stability of delayed memristive neural networks with time-varying impulses

Stability and synchronization for complex-valued neural networks with stochastic parameters and mixed time delays

In this paper, a class of complex-valued neural networks (CVNNs) with stochastic parameters and mixed time delays are proposed. The random fluctuation of system parameters is considered in order to describe the implementation of CVNNs more practically. Mixed time delays including distributed delays and time-varying delays are also taken into account in order to reflect the influence of network loads and communication constraints. Firstly, the stability problem is investigated for the CVNNs. In virtue of Lyapunov stability theory, a sufficient condition is deduced to ensure that CVNNs are asymptotically stable in the mean square. Then, for an array of coupled identical CVNNs with stochastic parameters and mixed time delays, synchronization issue is investigated. A set of matrix inequalities are obtained by using Lyapunov stability theory and Kronecker product and if these matrix inequalities are feasible, the addressed CVNNs are synchronized. Finally, the effectiveness of the obtained theoretical results is demonstrated by two numerical examples.

Fixed-time synchronization of delayed memristive neural networks with impulsive effects via novel fixed-time stability theorem

In this study, the fixed-time synchronization (FXTS) of delayed memristive neural networks (MNNs) with hybrid impulsive effects is explored. To investigate the FXTS mechanism, we first propose a novel theorem about the fixed-time stability (FTS) of impulsive dynamical systems, where the coefficients are extended to functions and the derivatives of Lyapunov function (LF) are allowed to be indefinite. After that, we obtain some new sufficient conditions for achieving FXTS of the system within a settling-time using three different controllers. At last, to verify the correctness and effectiveness of our results, a numerical simulation was conducted. Significantly, the impulse strength studied in this paper can take different values at different points, so it can be regarded as a time-varying function, unlike those in previous studies (the impulse strength takes the same value at different points). Hence, the mechanisms in this article are of more practical applicability.

Aperiodic switching event-triggered stabilization of continuous memristive neural networks with interval delays

The stabilization problem is studied for memristive neural networks with interval delays under aperiodic switching event-triggered control. Note that, most of delayed memristive neural networks models studied are discontinuous, which are not the real memristive neural networks. First, a real model of memristive neural networks is proposed by continuous differential equations, furthermore, it is simplified to neural networks with interval matrix uncertainties. Secondly, an aperiodic switching event-trigger is given, and the considered system switches between aperiodic sampled-data system and continuous event-triggered system. Thirdly, by constructing a time-dependent piecewise-defined Lyapunov functional, the stability criterion and the feedback gain design are obtained by linear matrix inequalities. Compared with the existing results, the stability criterion is with lower conservatism. Finally, two neurons are taken as examples to ensure the feasibility of the results.

H ∞ state estimation of quaternion-valued inertial neural networks: non-reduced order method

This paper concentrates on the problem of H ∞ state estimation for quaternion-valued inertial neural networks (QVINNs) with nonidentical time-varying delay. Without reducing the original second order system into two first order systems, a non-reduced order method is developed to investigate the addressed QVINNs, which is different from the majority of existing references. By constructing a new Lyapunov functional with tuning parameters, some easily checked algebraic criteria are established to ascertain the asymptotic stability of error-state system with the desired H ∞ performance. Moreover, an effective algorithm is provided to design the estimator parameters. Finally, a numerical example is given out to illustrate the feasibility of the designed state estimator.

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.

Synchronization Analysis of Inertial Memristive Neural Networks with Time-Varying Delays

This paper investigates the global exponential synchronization and quasi-synchronization of inertial memristive neural networks with time-varying delays. By using a variable transmission, the original second-order system can be transformed into first-order differential system. Then, two types of drive-response systems of inertial memristive neural networks are studied, one is the system with parameter mismatch, the other is the system with matched parameters. By constructing Lyapunov functional and designing feedback controllers, several sufficient conditions are derived respectively for the synchronization of these two types of drive-response systems. Finally, corresponding simulation results are given to show the effectiveness of the proposed method derived in this paper.

Passivity analysis of memristor-based impulsive inertial neural networks with time-varying delays

This paper focuses on delay-dependent passivity analysis for a class of memristive impulsive inertial neural networks with time-varying delays. By choosing proper variable transformation, the memristive inertial neural networks can be rewritten as first-order differential equations. The memristive model presented here is regarded as a switching system rather than employing the theory of differential inclusion and set-value map. Based on matrix inequality and Lyapunov-Krasovskii functional method, several delay-dependent passivity conditions are obtained to ascertain the passivity of the addressed networks. In addition, the results obtained here contain those on the passivity for the addressed networks without impulse effects as special cases and can also be generalized to other neural networks with more complex pulse interference. Finally, one numerical example is presented to show the validity of the obtained results.

O(t-α)-synchronization and Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations

This paper investigates O(t^-α)-synchronization and adaptive Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations. Firstly, based on the framework of Filippov solution and differential inclusion theory, using a Razumikhin-type method, some sufficient conditions ensuring the global O(t^-α)-synchronization of considered networks are established via a linear-type discontinuous control. Next, a new fractional differential inequality is established and two new discontinuous adaptive controller is designed to achieve Mittag-Leffler synchronization between the drive system and the response systems using this inequality. Finally, two numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized fractional-order memristive neural networks circuits involving discontinuous activations and time-varying delays.

Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays

This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.

Exponential Stability and Stabilization of Delayed Memristive Neural Networks Based on Quadratic Convex Combination Method

This paper is concerned with the exponential stability and stabilization of memristive neural networks (MNNs) with delays. First, we present some generalized double-integral inequalities, which include some existing inequalities as their special cases. Second, combining with quadratic convex combination method, these double-integral inequalities are employed to formulate a delay-dependent stability condition for MNNs with delays. Third, a state-dependent switching control law is obtained for MNNs with delays based on the proposed stability conditions. The desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities. Finally, the feasibility and effectiveness of the proposed results are tested by two numerical examples.

Event-based exponential synchronization of complex networks

In this paper, we consider exponential synchronization of complex networks. The information diffusions between nodes are driven by properly defined events. By employing the M-matrix theory, algebraic graph theory and the Lyapunov method, two kinds of distributed event-triggering laws are designed, which avoid continuous communications between nodes. Then, several criteria that ensure the event-based exponential synchronization are presented, and the exponential convergence rates are obtained as well. Furthermore, we prove that Zeno behavior of the event-triggering laws can be excluded before synchronization being achieved, that is, the lower bounds of inter-event times are strictly positive. Finally, a simulation example is provided to illustrate the effectiveness of theoretical analysis.

Stability and synchronization analysis of inertial memristive neural networks with time delays

This paper is concerned with the problem of stability and pinning synchronization of a class of inertial memristive neural networks with time delay. In contrast to general inertial neural networks, inertial memristive neural networks is applied to exhibit the synchronization and stability behaviors due to the physical properties of memristors and the differential inclusion theory. By choosing an appropriate variable transmission, the original system can be transformed into first order differential equations. Then, several sufficient conditions for the stability of inertial memristive neural networks by using matrix measure and Halanay inequality are derived. These obtained criteria are capable of reducing computational burden in the theoretical part. In addition, the evaluation is done on pinning synchronization for an array of linearly coupled inertial memristive neural networks, to derive the condition using matrix measure strategy. Finally, the two numerical simulations are presented to show the effectiveness of acquired theoretical results.

Passivity of memristor-based BAM neural networks with different memductance and uncertain delays

This paper addresses the passivity problem for a class of memristor-based bidirectional associate memory (BAM) neural networks with uncertain time-varying delays. In particular, the proposed memristive BAM neural networks is formulated with two different types of memductance functions. By constructing proper Lyapunov-Krasovskii functional and using differential inclusions theory, a new set of sufficient condition is obtained in terms of linear matrix inequalities which guarantee the passivity criteria for the considered neural networks. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theoretical results.

Function projective synchronization of memristor-based Cohen-Grossberg neural networks with time-varying delays

This paper deals with the problem of function projective synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, some novel criteria are obtained to realize the function projective synchronization of addressed networks by combining open loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the considered memristor-based Cohen-Grossberg neural network. Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the obtained results.

The stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms

The global asymptotic stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms is investigated. Under some suitable assumptions and using Lyapunov-Krasovskii functional method, we apply the linear matrix inequality technique to propose some new sufficient conditions for the global asymptotic stability of the addressed model in the stochastic sense. The mixed time delays comprise both the time-varying and continuously distributed delays. The effectiveness of the theoretical result is illustrated by a numerical example.

Stability analysis of memristor-based fractional-order neural networks with different memductance functions

In this paper, the problem of the existence, uniqueness and uniform stability of memristor-based fractional-order neural networks (MFNNs) with two different types of memductance functions is extensively investigated. Moreover, we formulate the complex-valued memristor-based fractional-order neural networks (CVMFNNs) with two different types of memductance functions and analyze the existence, uniqueness and uniform stability of such networks. By using Banach contraction principle and analysis technique, some sufficient conditions are obtained to ensure the existence, uniqueness and uniform stability of the considered MFNNs and CVMFNNs with two different types of memductance functions. The analysis results establish from the theory of fractional-order differential equations with discontinuous right-hand sides. Finally, four numerical examples are presented to show the effectiveness of our theoretical results.