Abstract The mean square exponential stability of stochastic time-delay neural networks (STDNNs) with random delayed impulses (RDIs) is addressed in this paper. Focusing on the variable delays in impulses, the notion of average random delay is adopted to consider these delays as a whole, and the stability criterion of STDNNs with RDIs is developed by using stochastic analysis idea and the Lyapunov method. Taking into account the impulsive effect, interference function and stabilization function of delayed impulses are explored independently. The results demonstrate that delayed impulses with random properties take a crucial role in dynamics of STDNNs, not only making stable STDNNs unstable, but also stabilizing unstable STDNNs. Our conclusions, specifically, allow for delays in both impulsive dynamics and continuous subsystems that surpass length of impulsive interval, which alleviates certain severe limitations, such as presence of upper bound for impulsive delays or requirement that impulsive delays can only exist between two impulsive events. Finally, feasibility of the theoretical results is verified through three simulation examples.

The time-triggered impulsive controls were widely used to study the collective behavior of homogeneous dynamical networks due to their low control cost, which was a bit conservative in the occupation of communication channels. This article addresses designing the event-triggered impulsive controls for the quasisynchronization, namely, a weak cooperative behavior with the synchronization error no more than a positive constant in the leader-following heterogeneous dynamical network, which thus can reduce the occupation of resources significantly. The centralized and distributed impulsive controls are designed to lead the followers to synchronize approximately to the leader within a nonzero bound, where the impulsive instants are triggered, respectively, by the global or local state-dependent conditions. Numerical results are put forward to verify the effectiveness of the proposed methods.

As the limits of transistor technology are approached, feature size in integrated circuit transistors has been reduced very near to the minimum physically-realizable channel length, and it has become increasingly difficult to meet expectations outlined by Moore’s law. As one of the most promising devices to replace transistors, memristors have many excellent properties that can be leveraged to develop new types of neural and non-von Neumann computing systems, which are expected to revolutionize information-processing technology. This survey provides a comparative overview of research progress on memristors. Different memristor synaptic devices are classified according to stimulation patterns and the working mechanisms of these various synaptic devices are analyzed in detail. Crossbar-based memristors have demonstrated advantages in physically executing vector-matrix multiplication and enabling highly power-efficient and area-efficient neuromorphic system designs. The extensive uses of crossbar-based memristors cover in-memory logic, vector-matrix multiplication, and many other fundamental computing operations. Furthermore, memristor-based architectures for efficient neural network training and inference have been studied. However, memristors have non-ideal properties due to programming inaccuracies and device imperfections from fabrication, which lead to error or mismatch in computed results. To build reliable memristor-based designs, circuit-level, algorithm-level, and system-level solutions to memristor reliability issues are being studied. To this end, state-of-the-art realizations of memristor crossbars, crossbar-based designs, and peripheral circuitry are presented, which show both promising full-system inference accuracy and excellent power efficiency in multiple tasks. Memristor in-situ learning benefits from high energy efficiency and biologically-imitative characteristics, which are conducive to further realizing hardware acceleration of cognitive learning. At present, the learning and training processes of brain-like networks are complex, presenting great challenges for network design and implementation.

This article shows a focus on the positivity and stability of Cohen-Grossberg-type time-delay memristor neural networks. We start by providing the existence and unique theorem of solutions for time-delay memristor neural networks to the case of unbounded delays. It is clear to find that the discriminate criterion of the existence and uniqueness of solutions about the argumented system with unbounded delays plays an important role in other related unbounded time-delay systems. Leveraging the Lyapunov method along with memristor nonlinearity, sufficient and necessary conditions for positivity and stability of Cohen-Grossberg-type memristor neural networks under unbounded delays are gained. Our proposed criteria don't need any strictly restrictive conditions. These theoretical results derived here will be helpful to understand the convergence performance of memristor electrical systems.

The observer design and H∞algorithm are proposed for the discrete-time fuzzy-logic systems in this article. The considered fuzzy-logic systems are subject to parameter uncertainty and unmeasurable state variables. To appropriately deal with parameter uncertainty and unmeasurable state variables, we first disintegrate the space of premise variables, then the total partitioned regions will be divided into two kinds: 1) crisp regions and 2) fuzzy regions. With the aid of partitioned regions, piecewise fuzzy H∞observers are presented. Availability of the piecewise fuzzy H∞observers gives us an accurate picture of the overall evolution of the augmented systems leading therefore to an improved situational awareness for the noncoordination of premise variables and external interference and, hence, the augmented systems achieve the performance conditions: asymptotic convergence and H∞performance. The simulation results of the proposed approach show the accuracy of the resulting state estimates.

In this article, the problems of finite-time/fixed-time synchronization have been investigated for discontinuous neural networks in the unified framework. To achieve the finite-time/fixed-time synchronization, a novel unified integral sliding-mode manifold is introduced, and corresponding unified control strategies are provided; some criteria are established for selecting suitable parameters for solving the related issue, namely, the dynamics of neural network can reach the designed sliding-mode manifold in finite/fixed time, and stay on it thereafter. Moreover, the estimations of setting time are given out. The established unified framework can bring in various protocols by choosing the different parameters of controllers and sliding-mode manifold, which extend previous related results. Finally, some numerical examples are introduced to show the effectiveness and superiority of resulting conclusions.

In this article, it addresses the problem of finite-/fixed-time synchronization of delayed coupled discontinuous neural networks in the unified framework. To achieve the finite-/fixed-time synchronization and precise estimations of setting time, two novel different kinds of controllers are established, in which one is switching. Then, based on the finite-/fixed-time theorem and Lyapunov function theory, some useful criteria are obtained to select suitable controllers' parameters, which can guarantee error systems converge in the finite time/fixed time with respect to coupled neural networks. Moreover, corresponding estimations of the setting time are also provided. Finally, two numerical examples are introduced to show the effectiveness of the proposed control protocols.

According to conventional memristive neural network theories, neurodynamic properties are powerful tools for solving many problems in the areas of brain-like associative learning, dynamic information storage or retrieval, etc. However, as have often been noted in most fractional-order systems, system analysis approaches for integral-order systems could not be directly extended and applied to deal with fractional-order systems, and consequently, it raises difficult issues in analyzing and controlling the fractional-order memristive neural networks. By using the set-valued maps and fractional-order differential inclusions, then aided by a newly proposed fractional derivative inequality, this paper investigates the global Mittag-Leffler stabilization for a class of fractional-order memristive neural networks. Two types of control rules (i.e., state feedback stabilizing control and output feedback stabilizing control) are designed for the stabilization of fractional-order memristive neural networks, while a list of stabilization criteria is established. Finally, two numerical examples are given to show the effectiveness and characteristics of the obtained theoretical results.

In this paper, we investigate a general class of fuzzy neurodynamic systems with piecewise constant argument of generalized type. Meanwhile, the time-varying input is under consideration. The pseudo-equilibria of this new type of neurodynamic systems is formulated and studied. Several sufficient conditions are obtained to ensure the existence and uniqueness of solutions. In addition, the global output convergence of such neurodynamic system is examined in detail. Several simulation examples are also given to verify the effectiveness of theoretical property and a potential application in analog associative memory.

In this paper, a new intelligence paradigm scheme to forecast landslide based on functional networks is presented. Both methodology and learning algorithm for this kind of intelligence system paradigm using the minimax method are derived. The performance and validity of the new functional networks intelligence paradigm are demonstrated by using real-world example. The results show that the landslide prediction using functional networks is reasonable, effective and achieves a high-quality performance.

Memristive neural systems are a groundbreaking concept that is helping to understand the behavior of many physical, technical and bionic systems. This paper reviews the research status of memristive neural systems in the past few years. Considering there are too many publications about the memristive neural systems, we summarize the relevant models and applications rather than contemplating to go into details of particular results. First, some representative models of memristive neural systems are simply introduced. Then, we briefly describe some novel applications in the related fields (dynamic information storage or retrieval, logical operations and ultra-high-performance computing). Subsequently, some existing problems are summarized, and finally, the trend of memristive neural systems is pointed out.

Memristive neuromorphic system is a good candidate for creating artificial brain. In this paper, a general class of memristive neural networks with discrete and distributed delays is introduced and studied. Some Lagrange stability criteria dependent on the network parameters are derived via nonsmooth analysis and control theory. In particular, several succinct criteria are provided to ascertain the Lagrange stability of memristive neural networks with and without delays. The proposed Lagrange stability criteria are the improvement and extension of the existing results in the literature. Three numerical examples are given to show the superiority of theoretical results.

In this paper, a general class of hybrid Lotka-Volterra recurrent neural networks with memristor characteristics is formulated and studied. Some sufficient conditions on nondivergence, global attractivity and complete stability of the network are obtained, respectively. These results can be applied to the memristive dynamic memories. The analysis in the paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. These theoretical analysis can characterize the fundamental electrical properties of memristor devices and provide convenience for applications. A numerical example is given to illustrate the theoretical findings via computer simulations.

In this paper, a general class of memristive neural networks with time delays is formulated and studied. Some sufficient conditions in terms of linear matrix inequalities are obtained, in order to achieve exponential stabilization. The result can be applied to the closed-loop control of memristive systems. In particular, several succinct criteria are given to ascertain the exponential stabilization of memristive cellular neural networks. In addition, a simplified and effective algorithm is considered for design of the optimal controller. These conditions are the improvement and extension of the existing results in the literature. Two numerical examples are given to illustrate the theoretical results via computer simulations.