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

A delay-dividing approach to robust stability of uncertain stochastic complex-valued Hopfield delayed neural networks

In scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study, a delay-dividing approach is devised to study the robust stability issue of uncertain neural networks. Specifically, the uncertain stochastic complex-valued Hopfield neural network (USCVHNN) with time delay is investigated. Here, the uncertainties of the system parameters are norm-bounded. Based on the Lyapunov mathematical approach and homeomorphism principle, the sufficient conditions for the global asymptotic stability of USCVHNN are derived. To perform this derivation, we divide a complex-valued neural network (CVNN) into two parts, namely real and imaginary, using the delay-dividing approach. All the criteria are expressed by exploiting the linear matrix inequalities (LMIs). Based on two examples, we obtain good theoretical results that ascertain the usefulness of the proposed delay-dividing approach for the USCVHNN model

Novel fixed-time stabilization of quaternion-valued BAMNNs with disturbances and time-varying coefficients

In this paper, with the quaternion number and time-varying coefficients introduced into traditional BAMNNs, the model of quaternion-valued BAMNNs are formulated. For the first time, fixed-time stabilization of time-varying quaternion-valued BAMNNs is investigated. A novel fixed-time control method is adopted, in which the choice of the Lyapunov function is more general than in most previous results. To cope with the noncommutativity of the quaternion multiplication, two different fixed-time control methods are provided, a decomposition method and a non-decomposition method. Furthermore, to reduce the control strength and improve control efficiency, an adaptive fixed-time control strategy is proposed. Lastly, numerical examples are presented to demonstrate the effectiveness of the theoretical results. © 2020 the Author(s), licensee AIMS Press

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

Finite-time adaptive synchronization of fractional-order delayed quaternion-valued fuzzy neural networks

Based on direct quaternion method, this paper explores the finite-time adaptive synchronization (FAS) of fractional-order delayed quaternion-valued fuzzy neural networks (FODQVFNNs). Firstly, a useful fractional differential inequality is created, which offers an effective way to investigate FAS. Then two novel quaternion-valued adaptive control strategies are designed. By means of our newly proposed inequality, the basic knowledge about fractional calculus, reduction to absurdity as well as several inequality techniques of quaternion and fuzzy logic, several sufficient FAS criteria are derived for FODQVFNNs. Moreover, the settling time of FAS is estimated, which is in connection with the order and initial values of considered systems as well as the controller parameters. Ultimately, the validity of obtained FAS criteria is corroborated by numerical simulations

Global exponential convergence of delayed inertial Cohen–Grossberg neural networks

In this paper, the exponential convergence of delayed inertial Cohen–Grossberg neural networks (CGNNs) is studied. Two methods are adopted to discuss the inertial CGNNs, one is expressed as two first-order differential equations by selecting a variable substitution, and the other does not change the order of the system based on the nonreduced-order method. By establishing appropriate Lyapunov function and using inequality techniques, sufficient conditions are obtained to ensure that the discussed model converges exponentially to a ball with the prespecified convergence rate. Finally, two simulation examples are proposed to illustrate the validity of the theorem results

Dissipativity analysis of stochastic fuzzy neural networks with randomly occurring uncertainties using delay dividing approach

This paper focuses on the problem of delay-dependent robust dissipativity analysis for a class of stochastic fuzzy neural networks with time-varying delay. The randomly occurring uncertainties under consideration are assumed to follow certain mutually uncorrelated Bernoulli-distributed white noise sequences. Based on the Itô's differential formula, Lyapunov stability theory, and linear matrix inequalities techniques, several novel sufficient conditions are derived using delay partitioning approach to ensure the dissipativity of neural networks with or without time-varying parametric uncertainties. It is shown, by comparing with existing approaches, that the delay-partitioning projection approach can largely reduce the conservatism of the stability results. Numerical examples are constructed to show the effectiveness of the theoretical results

A switching control for finite-time synchronization of memristor-based BAM neural networks with stochastic disturbances

This paper deals with the finite-time stochastic synchronization for a class of memristorbased bidirectional associative memory neural networks (MBAMNNs) with time-varying delays and stochastic disturbances. Firstly, based on the physical property of memristor and the circuit of MBAMNNs, a MBAMNNs model with more reasonable switching conditions is established. Then, based on the theory of Filippov’s solution, by using Lyapunov–Krasovskii functionals and stochastic analysis technique, a sufficient condition is given to ensure the finite-time stochastic synchronization of MBAMNNs with a certain controller. Next, by a further discussion, an errordependent switching controller is given to shorten the stochastic settling time. Finally, numerical simulations are carried out to illustrate the effectiveness of theoretical results

Finite-time lag projective synchronization of delayed fractional-order quaternion-valued neural networks with parameter uncertainties

This paper discusses a class issue of finite-time lag projective synchronization (FTLPS) of delayed fractional-order quaternion-valued neural networks (FOQVNNs) with parameter uncertainties, which is solved by a non-decomposition method. Firstly, a new delayed FOQVNNs model with uncertain parameters is designed. Secondly, two types of feedback controller and adaptive controller without sign functions are designed in the quaternion domain. Based on the Lyapunov analysis method, the non-decomposition method is applied to replace the decomposition method that requires complex calculations, combined with some quaternion inequality techniques, to accurately estimate the settling time of FTLPS. Finally, the correctness of the obtained theoretical results is testified by a numerical simulation example