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

Global exponential synchronization of quaternion-valued memristive neural networks with time delays

This paper extends the memristive neural networks (MNNs) to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established, and the problem of drive-response global synchronization of this type of networks is investigated in this paper. Two cases are taken into consideration: one is with the conventional differential inclusion assumption, the other without. Criteria for the global synchronization of these two cases are achieved respectively by appropriately choosing the Lyapunov functional and applying some inequality techniques. Finally, corresponding simulation examples are presented to demonstrate the correctness of the proposed results derived in this paper

General decay lag anti-synchronization of multi-weighted delayed coupled neural networks with reaction–diffusion terms

We propose a new anti-synchronization concept, called general decay lag anti-synchronization, by combining the definitions of decay synchronization and lag synchronization. Novel criteria for the decay lag anti-synchronization of multi-weighted delayed coupled reaction–diffusion neural networks (MWDCRDNNs) with and without bounded distributed delays are derived by constructing an appropriate nonlinear controller and using the Lyapunov functional method. Moreover, the robust decay lag anti-synchronization of MWDCRDNNs with and without bounded distributed delays is considered. Finally, two numerical simulations are performed to validate the obtained results

Finite-time Anti-synchronization of Memristive Stochastic BAM Neural Networks with Probabilistic Time-varying Delays

This paper investigates the drive-response finite-time anti-synchronization for memristive bidirectional associative memory neural networks (MBAMNNs). Firstly, a class of MBAMNNs with mixed probabilistic time-varying delays and stochastic perturbations is first formulated and analyzed in this paper. Secondly, an nonlinear control law is constructed and utilized to guarantee drive-response finite-time anti-synchronization of the neural networks. Thirdly, by employing some inequality technique and constructing an appropriate Lyapunov function, some anti-synchronization criteria are derived. Finally, a number simulation is provided to demonstrate the effectiveness of the proposed mechanism

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

New results on finite-/fixed-time synchronization of delayed memristive neural networks with diffusion effects

In this paper, we further investigate the finite-/fixed-time synchronization (FFTS) problem for a class of delayed memristive reaction-diffusion neural networks (MRDNNs). By utilizing the state-feedback control techniques, and constructing a general Lyapunov functional, with the help of inequality techniques and the finite-time stability theory, novel criteria are established to realize the FFTS of the considered delayed MRDNNs, which generalize and complement previously known results. Finally, a numerical example is provided to support the obtained theoretical results

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

Passivity and synchronization of coupled reaction-diffusion complex-valued memristive neural networks

This paper considers two types of coupled reaction-diffusion complex-valued memristive neural networks (CRDCVMNNs). The nodes of the first type CRDCVMNN are coupled through their state and the second one is coupled by spatial diffusion coupling term. For the former, some novel criteria for the passivity and synchronization are derived by constructing an appropriate controller and utilizing some inequality techniques as well as Lyapunov functional method. For the latter, we establish some sufficient conditions which guarantee that this type of CRDCVMNNs can realize passivity and synchronization. Finally, the effectiveness and correctness of the acquired theoretical results are verified by two numerical examples

Event-triggered passivity of multi-weighted coupled delayed reaction-diffusion memristive neural networks with fixed and switching topologies

This paper solves the event-triggered passivity problem for multiple-weighted coupled delayed reaction-diffusion memristive neural networks (MWCDRDMNNs) with fixed and switching topologies. On the one side, by designing appropriate event-triggered controllers, several passivity criteria for MWCDRDMNNs with fixed topology are derived based on the Lyapunov functional method and some inequality techniques. Moreover, some adequate conditions for ensuring asymptotical stability of the event-triggered passive network are presented. On the other side, we take the switching topology in network model into consideration, and investigate the event-triggered passivity and passivity-based synchronization for MWCDRDMNNs with switching topology. Finally, two examples with numerical simulation results are provided to illustrate the effectiveness of the obtained theoretical results