This article investigates the mean square exponential stability for dynamic memristor-neutral stochastic cellular neural networks with time-varying delays (DM-NSDCNNs). Unlike general neural networks (NNs) analyzed in the voltage-current domain, DM-NSDCNNs are studied in the flux-charge domain, offering a significant advantage: all current, voltage, and power consumption vanish when the system reaches a steady state. In particular, dynamic memristor store the results of computation. To better utilize these properties, two distinct stochastic stability analysis techniques are considered, depending on the memristor's constitutive relations. For piecewise linear constitutive relation, the stability criteria are obtained by a novel approach based on the comparison principle and reductio ad absurdum. Moreover, the stability criteria for cubic nonlinear constitutive relation are established via stochastic analysis employing Lyapunov functional techniques. Finally, several numerical examples with different constitutive relations of DM-NSDCNNs are provided to verify the effectiveness and potential of the proposed results.

In this article, the synchronization problem of memristive neural networks (MNNs) subjected to multiple failures is investigated. First, a general form of fault model is introduced into the MNNs, which can represent and summarize various process faults, actuator faults, and their coupling. Subsequently, with the help of designing intermediate variables, two types of fault function observers based on state feedback and output feedback are constructed, and their effectiveness is verified through a generalization of Halanay-type inequalities. Then, based on the designed observers and the event-triggered strategy, two classes of fault-tolerant synchronization schemes are designed for the considered MNNs. By adjusting the controller parameter conditions, finite-time and fixed-time synchronization or quasi-synchronization of the considered MNNs system can be achieved, respectively. Finally, the effectiveness of the provided fault observers and synchronization strategies is verified through simulation and comparison experiments.

This article investigates the finite-time stabilization problem of inertial memristive neural networks (IMNNs) with bounded and unbounded time-varying delays, respectively. To simplify the theoretical derivation, the nonreduced order method is utilized for constructing appropriate comparison functions and designing a discontinuous state feedback controller. Then, based on the controller, the state of IMNNs can directly converge to 0 in finite time. Several criteria for finite-time stabilization of IMNNs are obtained and the setting time is estimated. Compared with previous studies, the requirement of differentiability of time delay is eliminated. Finally, numerical examples illustrate the usefulness of the analysis results in this article.

This article examines the finite-time (F-T) synchronization issue for a class of recurrent neural networks (NNs) that have, respectively, bounded and unbounded time-varying delays. First, two novel F-T stability lemmas are presented in the form of generalized Halanay inequalities. Second, based on the obtained lemmas, some simple and easy-to-use F-T synchronization criteria are rendered for the considered NNs under two different Lyapunov functions. The results obtained in this article greatly reduce system constraints and are therefore more applicable. The validity of the theoretical results derived in this article is finally checked using three numerical instances.

This article focuses on the fixed-time bipartite consensus problems of multiagent systems under time-varying disconnected topologies. Different from the jointly connected topology, an enhanced fixed-time local pinning algorithm is proposed to overcome challenges posed by disconnected signed networks without introducing additional topological assumptions. Especially, the motion tendencies of isolated agents in cooperative-competitive networks are thoroughly discussed. Event-triggered control with the impulsive effect is utilized to achieve the bipartite consensus of MASs with minimal energy consumption, where the total energy function does not need to be monotonic, and the Zeno behavior can be avoided. Finally, the efficacy of the designed protocol is demonstrated through two numerical examples.

In dynamic systems with communication limitations and delay, the input-to-state stability (ISS) is crucial for ensuring system performance. In this article, the finite-time ISS (FTISS) of time-delay neural networks (NNs) with disturbances is investigated. First, by further considering the idea of finite-time contractive stability (FTCS), the prescribed performance is proposed for the considered NNs system, thereby achieving better learning ability and robustness. Next, in order to achieve the above research objectives, some stability conditions for the considered NNs with disturbances are given by constructing sequentially two classes of Lyapunov functions and a finite-time contractive function. Subsequently, a stabilization strategy is proposed to further reduce the parameter requirements of the NNs system and improve its application value. Finally, the numerical simulation and comparative experiments have verified the effectiveness of the stability strategy provided in this article.

By using the fault-tolerant control method, the synchronization of memristive neural networks (MNNs) subjected to multiple actuator failures is investigated in this article. The considered actuator failures include the effectiveness failure and the lock-in-place failure, which are different from previous results. First of all, the mathematical expression of the control inputs in the considered system is given by introducing the models of the above two types of actuator failures. Following, two classes of synchronization strategies, which are state feedback control strategies and event-triggered control strategies, are proposed by using some inequality techniques and Lyapunov stability theories. The designed controllers can, respectively, guarantee the realization of synchronizations of the global exponential, the finite-time and the fixed-time for the MNNs by selecting different parameter conditions. Then the estimations of settling times of provided synchronization schemes are computed and the Zeno phenomenon of proposed event-triggered strategies is explicitly excluded. Finally, two experiments are conducted to confirm the availability of given synchronization strategies.

As quaternion-valued memristor neural networks (MNNs) have important applications in many engineering fields and the information in the real world is often uncertain and inaccurate, therefore, in order to better apply to practice, it is necessary to study the dynamic behaviors of quaternion-valued MNNs with fuzzy logic. In this article, the event-based synchronization problem for quaternion-valued Takagi–Sugeno (T-S) fuzzy MNNs (QVT-SFMNNs) with time-varying delays is studied. Different from the existing synchronization results of MNNs, T-S fuzzy logic and quaternion are simultaneously considered in the MNNs, which makes the model more applicable. Based on some algebraic properties of quaternions, a novel event-based fuzzy controller and some static and dynamic event trigger conditions are designed. By constructing simple Lyapunov functions instead of complex Lyapunov functionals and using Halanay inequality, several sufficient criteria are given to ensure the global exponential synchronization between the considered QVT-SFMNNs. Meanwhile, the Zeno behaviors of the response QVT-SFMNN under different event trigger conditions are excluded. It is important to note that the results obtained in article are less conservative and applicable to low-dimensional complex-valued and real-valued MNNs. Finally, a numerical example is given to verify the validity of the obtained theoretical results.

This article concentrates on the global exponential synchronization problem of multiple neural networks with time delay by the event-based output quantized coupling control method. In order to reduce the signal transmission cost and avoid the difficulty of obtaining the systems' full states, this article adopts the event-triggered control and output quantized control. A new dynamic event-triggered mechanism is designed, in which the control parameters are time-varying functions. Under weakened coupling matrix conditions, by using a Halanay-type inequality, some simple and easily verified sufficient conditions to ensure the exponential synchronization of multiple neural networks are presented. Moreover, the Zeno behaviors of the system are excluded. Some numerical examples are given to verify the effectiveness of the theoretical analysis in this article.

This article investigates a generalized type of multistability about almost periodic solutions for memristive Cohen–Grossberg neural networks (MCGNNs). As the inevitable disturbances in biological neurons, almost periodic solutions are more common in nature than equilibrium points (EPs). They are also generalizations of EPs in mathematics. According to the concepts of almost periodic solutions and$\Psi$-type stability, this article presents a generalized-type multistability definition of almost periodic solutions. The results show that$(K+1)^n$generalized stable almost periodic solutions can coexist in a MCGNN with$n$neurons, where$K$is a parameter of the activation functions. The enlarged attraction basins are also estimated based on the original state space partition method. Some comparisons and convincing simulations are given to verify the theoretical results at the end of this article.

This article is devoted to analyzing the multistability and robustness of competitive neural networks (NNs) with time-varying delays. Based on the geometrical structure of activation functions, some sufficient conditions are proposed to ascertain the coexistence of equilibrium points, of them are locally exponentially stable, where represents a dimension of system and is the parameter related to activation functions. The derived stability results not only involve exponential stability but also include power stability and logarithmical stability. In addition, the robustness of stable equilibrium points is discussed in the presence of perturbations. Compared with previous papers, the conclusions proposed in this article are easy to verify and enrich the existing stability theories of competitive NNs. Finally, numerical examples are provided to support theoretical results.

This article considers some further results on fixed-time leader-following consensus of disturbed heterogeneous multiagent systems (DHMASs). Both the first-order (FO) nonlinear nodes and second-order (SO) ones are contained in the considered system model. First, a distributed observer is developed to ensure the estimated states converge to the leader’s real states under a directed graph. Second, an integral sliding mode controller (SMC) is proposed to guarantee the predefined-time consensus (PTC) of FO agents based on the Gudermannian functions. Third, a nonsingular terminal SMC is given to realize consensus of SO agents in a predefined time. It is pointed out that, both the reaching and sliding time can be preset as to the task requirements. Finally, the effectiveness of new designs are illustrated by two numerical examples.

This article mainly studies the multistability of complex-valued neural networks (CVNNs) with general periodic-type activation functions. In order to improve the storage capacity of associative memory, a general periodic-type activation function is introduced which obtains three different numbers of equilibrium points (EPs), including unique, finite, and countable infinite. The existence and stability of equilibria are investigated based on Brouwer’s fixed point theorem andM-matrix method. By means of a sign function on complex numbers, stability is confirmed using a new norm on the absolute values of the real and imaginary parts. The attraction basins of exponentially stable equilibria are estimated, which are bigger than the subspaces of the original division. Also, the design of associative memory is given. Finally, two numerical simulation examples verify the obtained results.

This brief discusses the reachable set estimation (RSE) problem for memristive neural networks (MNNs) involving time-varying delays and bounded disturbances. The reachable sets of the considered MNNs under zero and nonzero initial conditions are estimated by two novel algebraic criteria, respectively. Compared with the existing results, the conclusions are easy to verify, and the obtained reachable sets are more accurate. Finally, the validity of the theoretical results is illustrated by two examples.

This article discusses the coexistence and dynamical behaviors of multiple equilibrium points (Eps) for fractional-order complex-valued memristive neural networks (FCVMNNs) with delays. First, based on the state space partition method, some sufficient conditions are proposed to guarantee that there are multiple Eps in one FCVMNN. Then, the Mittag-Leffler stability of those multiple Eps is proved by using the Lyapunov function. Simultaneously, the enlarged attraction basins are obtained to improve and extend the existing theoretical results in the previous literature. In addition, some existing stability results in the literature are special cases of a new result herein. Finally, two illustrative examples with computer simulations are presented to verify the effectiveness of theoretical analysis.

In this article, the global asymptotic stability of a class of recurrent neural networks (RNNs) with generalized piecewise constant argument (GPCA) is investigated. By the Banach fixed point theorem (BFPT) and comparison principle, a set of improved criteria are presented to guarantee the existence and uniqueness (EU) of the solutions and global asymptotic stability of equilibrium point for the considered RNNs. Compared with the existing results, this article not only reduces the requirements for system parameters, but also provides more criteria in different forms, which greatly improve the feasible range of the obtained criteria. The effectiveness of the obtained results are tested by some numerical examples.

This article aims at analyzing and designing the multivalued high-capacity-associative memories based on recurrent neural networks with both asynchronous and distributed delays. In order to increase storage capacities, multivalued activation functions are introduced into associative memories. The stored patterns are retrieved by external input vectors instead of initial conditions, which can guarantee accurate associative memories by avoiding spurious equilibrium points. Some sufficient conditions are proposed to ensure the existence, uniqueness, and global exponential stability of the equilibrium point of neural networks with mixed delays. For neural networks with${n}$neurons,${m}$-dimensional input vectors, and${2k}$-valued activation functions, the autoassociative memories have${(2k)^{n}}$storage capacities and heteroassociative memories have min${\{(2k)^{n},(2k)^{m}\}}$storage capacities. That is, the storage capacities of designed associative memories in this article are obviously higher than the${2^{n}}$and min${\{2^{n},2^{m}\}}$storage capacities of the conventional ones. Three examples are given to support the theoretical results.

This article investigates hardware implementation of hierarchical temporal memory (HTM), a brain-inspired machine learning algorithm that mimics the key functions of the neocortex and is applicable to many machine learning tasks. Spatial pooler (SP) is one of the main parts of HTM, designed to learn the spatial information and obtain the sparse distributed representations (SDRs) of input patterns. The other part is temporal memory (TM) which aims to learn the temporal information of inputs. The memristor, which is an appropriate synapse emulator for neuromorphic systems, can be used as the synapse in SP and TM circuits. In this article, a memristor-based SP (MSP) circuit structure is designed to accelerate the execution of the SP algorithm. The presented MSP has properties of modeling both the synaptic permanence and the synaptic connection state within a single synapse, and on-device and parallel learning. Simulation results of statistic metrics and classification tasks on several real-world datasets substantiate the validity of MSP.

Most existing finite-/fixed-time synchronization control schemes are nonsmooth or discontinuous, and the settling time is estimated with conservatism. It is due to the utilization of signum function or fraction power state feedback. This brief considers the problem of prespecified-time cluster synchronization of complex networks with a smooth control protocol. The synchronization time is independent of any control parameters or any systems' initial conditions, which is actually uniformly prescribed according to task requirements without any estimations. Moreover, the cluster synchronization can maintain after the specified time, and the smooth control input can always keep uniformly bounded in an infinite time interval as well. Finally, one numerical example is provided to illustrate the effectiveness of the proposed protocol and design method.

This brief proposes a unified theoretical framework to investigate the finite/fixed-time synchronization of complex networks with stochastic disturbances. By designing a common pinning controller with different ranges of power parameters, both the goals of finite-time and fixed-time synchronization in probability for the network topology containing spanning trees can be achieved. Moveover, with the help of finite-time stochastic stability theory, two types of explicit expressions of finite/fixed (dependent/independent on the initial values) settling times are calculated as well. One numerical example is finally presented to demonstrate the effectiveness of the theoretical analysis.

This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.

This paper is concerned with the finite-time synchronization (FTS) issue of switched coupled neural networks with discontinuous or continuous activations. Based on the framework of nonsmooth analysis, some discontinuous or continuous controllers are designed to force the coupled networks to synchronize to an isolated neural network. Some sufficient conditions are derived to ensure the FTS by utilizing the well-known finite-time stability theorem for nonlinear systems. Compared with the previous literatures, such synchronization objective will be realized when the activations and the controllers are both discontinuous. The obtained results in this paper include and extend the earlier works on the synchronization issue of coupled networks with Lipschitz continuous conditions. Moreover, an upper bound of the settling time for synchronization is estimated. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

In this paper, we study the problem of finite-time consensus of multiagent systems on a fixed directed interaction graph with a new protocol. Existing finite-time consensus protocols can be divided into two types: 1) continuous and 2) discontinuous, which were studied separately in the past. In this paper, we deal with both continuous and discontinuous protocols simultaneously, and design a centralized switching consensus protocol such that the finite-time consensus can be realized in a fast speed. The switching protocol depends on the range of the initial disagreement of the agents, for which we derive an exact bound to indicate at what time a continuous or a discontinuous protocol should be selected to use. Finally, we provide two numerical examples to illustrate the superiority of the proposed protocol and design method.

This paper investigates quasi-synchronization of switched linearly coupled complex networks with discontinuous nonlinear functions. The existence and boundedness of solutions for discontinuous complex networks are derived by the matrix measure approach and Filippov solutions. A sufficient condition is derived to ensure quasi-synchronization of switched coupled complex networks with discontinuous isolated nodes, which could be controlled by some designed linear controllers. The main results extend the previous work on the synchronization issue of coupled switched networks with Lipschitz continuous conditions. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.

Discontinuous dynamical systems, particularly neural networks with discontinuous activation functions, arise in a number of applications and have received considerable research attention in recent years. In this paper, the robust state estimation problem is investigated for uncertain neural networks with discontinuous activations and time-varying delays, where the neuron-dependent nonlinear disturbance on the network outputs are only assumed to satisfy the local Lipschitz condition. Based on the theory of differential inclusions and nonsmooth analysis, several criteria are presented to guarantee the existence of the desired robust state estimator for the discontinuous neural networks. It is shown that the design of the state estimator for such networks can be achieved by solving some linear matrix inequalities, which are dependent on the size of the time derivative of the time-varying delays. Finally, numerical examples are given to illustrate the theoretical results.