This article considers both the semi-Markov jumping phenomenon and spatial distribution characteristics when investigating the exponential stabilization of memristive neural networks (MNNs). The introduction of the semi-Markov jumping parameters relaxes the restriction on the sojourn time of Markovian MNNs. To increase the operability while ensuring control effect, a novel event-based spatially pointwise-piecewise switching control scheme is presented under a unified spatial division criterion, in which the pointwise and piecewise control can switch according to the preset event condition for the applicability to different control requirements. Moreover, by constructing a semi-Markov Lyapunov functional and utilizing the properties of the considered cumulative distribution function, the final exponential stabilization criterion and two related corollaries are obtained. Finally, simulation results illustrate the effectiveness and superiority of the proposed control strategy.

Master-slave synchronization of two delayed neural networks with adaptive controller has been studied in recent years; however, the existing delays in network models are bounded or unbounded with some derivative constraints. For more general delay without these restrictions, how to design proper adaptive controller and prove rigorously the convergence of error system is still a challenging problem. This article gives a positive answer for this problem. By means of the stability result of unbounded delayed system and some analytical techniques, we prove that the traditional centralized adaptive algorithms can achieve global asymptotical synchronization even if the network delays are unbounded without any derivative constraints. To describe the convergence speed of the synchronization error, adaptive designs depending on a flexible ω -type function are also provided to control the synchronization error, which can lead exponential synchronization, polynomial synchronization, and logarithmically synchronization. Numerical examples on delayed neural networks and chaotic Ikeda-like oscillator are presented to verify the adaptive designs, and we find that in the case of unbounded delay, the intervention of ω -type function can promote the realization of synchronization but may destroy the convergence of control gain, and this however will not happen in the case of bounded delay.

This article is concerned with fractional-order discontinuous complex-valued neural networks (FODCNNs). Based on a new fractional-order inequality, such system is analyzed as a compact entirety without any decomposition in the complex domain which is different from a common method in almost all literature. First, the existence of global Filippov solution is given in the complex domain on the basis of the theories of vector norm and fractional calculus. Successively, by virtue of the nonsmooth analysis and differential inclusion theory, some sufficient conditions are developed to guarantee the global dissipativity and quasi-Mittag-Leffler synchronization of FODCNNs. Furthermore, the error bounds of quasi-Mittag-Leffler synchronization are estimated without reference to the initial values. Especially, our results include some existing integer-order and fractional-order ones as special cases. Finally, numerical examples are given to show the effectiveness of the obtained theories.

In this article, master-slave synchronization of reaction-diffusion neural networks (RDNNs) with nondifferentiable delay is investigated via the adaptive control method. First, centralized and decentralized adaptive controllers with state coupling are designed, respectively, and a new analytical method by discussing the size of adaptive gain is proposed to prove the convergence of the adaptively controlled error system with general delay. Then, spatial coupling with adaptive gains depending on the diffusion information of the state is first proposed to achieve the master-slave synchronization of delayed RDNNs, while this coupling structure was regarded as a negative effect in most of the existing works. Finally, numerical examples are given to show the effectiveness of the proposed adaptive controllers. In comparison with the existing adaptive controllers, the proposed adaptive controllers in this article are still effective even if the network parameters are unknown and the delay is nonsmooth, and thus have a wider range of applications.

This article considers the quasisynchronization of memristive neural networks (MNNs) with communication delays via event-triggered impulsive control (ETIC). In view of the limited communication and bandwidth, we adopt a novel switching event-triggered mechanism (ETM) that not only decreases the times of controller update and the amount of data sent out but also eliminates the Zeno behavior. By using an appropriate Lyapunov function, several algebraic conditions are given for quasisynchronization of MNNs with communication delays. More important, there is no restriction on the derivation of the Lyapunov function, even if it is an increasing function over a period of time. Then, we further propose a switching ETM depending on communication delays and aperiodic sampling, which is more economical and practical and can directly avoid Zeno behavior. Finally, two simulations are presented to validate the effectiveness of the proposed results.

This article investigates the stability and synchronization of nonautonomous reaction-diffusion neural networks with general time-varying delays. Compared with the existing works concerning reaction-diffusion neural networks, the main innovation of this article is that the network coefficients are time-varying, and the delays are general (which means that fewer constraints are posed on delays; for example, the commonly used conditions of differentiability and boundedness are no longer needed). By Green's formula and some analytical techniques, some easily checkable criteria on stability and synchronization for the underlying neural networks are established. These obtained results not only improve some existing ones but also contain some novel results that have not yet been reported. The effectiveness and superiorities of the established criteria are verified by three numerical examples.

This paper considers the self-synchronization and tracking synchronization issues for a class of nonidentically coupled neural networks model with unknown parameters and diffusion effects. Using the special structure of neural networks with global Lipschitz activation function, nonidentical terms are treated as external disturbances, which can then be compensated via robust adaptive control techniques. For the case where no common reference trajectory is given in advance, a distributed adaptive controller is proposed to drive the synchronization error to an adjustable bounded area. For the case where a reference trajectory is predesigned, two distributed adaptive controllers are proposed, respectively, to address the tracking synchronization problem with bounded and unbounded reference trajectories, different decomposition methods are given to extract the heterogeneous characteristics. To avoid the appearance of global information, such as the spectrum of the coupling matrix, corresponding adaptive designs on coupling strengths are also provided for both cases. Moreover, the upper bounds of the final synchronization errors can be gradually adjusted according to the parameters of the adaptive designs. Finally, numerical examples are given to test the effectiveness of the control algorithms.

This paper investigates the quasi-synchronization of delayed memristive neural networks (MNNs) via a novel hybrid impulsive control algorithm which combines time-triggered and event-triggered impulsive control. The relationship between a predesigned non-negative auxiliary function and a given exponentially decreasing threshold function is used to describe the switching. Under this novel controller, sufficient conditions for the quasi-synchronization are derived by the impulsive differential inequality. In addition, by choosing appropriate parameters or initial conditions such that the initial value of the non-negative auxiliary function is less than that of the event-triggered function, the quasi-synchronization can be realized theoretically as long as the event-triggered impulsive intensity is less than 1. This greatly reduces the conservatism of the existing quasi-synchronization results. Furthermore, the event-triggered rules can avoid the Zeno behavior as long as the event-triggered impulsive intensity is less than 1. This hybrid mechanism can reduce the amount of impulsive control and lessen the network communication. Finally, one example is given to illustrate the validness of the obtained results.

This paper investigates the φ-type stability and robust stability for a general class of stochastic reaction-diffusion neural networks (SRDNNs) with Dirichlet boundary conditions, infinite discrete time-varying delays, and infinite continuously distributed delays. By virtue of inequality techniques, properties of M-matrix, and theories of stochastic analysis, several sufficient criteria are obtained to guarantee the almost sure φ-type stability, pth moment φ-type stability, and φ-type robust stability of the underlying SRDNNs with hybrid unbounded time delays. With appropriate choices of the function φ, the φ-type stability reduces to the exponential stability, polynomial stability, and logarithmic stability. Additionally, the developed results herein include some existing ones as special cases. A numerical simulation is performed to substantiate the effectiveness and superiority of the theoretical analysis.

The synchronization problem of multiple/coupled reaction-diffusion neural networks with time-varying delays is investigated. Differing from the existing considerations, state delays among distinct neurons and coupling delays among different subnetworks are included in the proposed model, the assumptions posed on the arisen delays are very weak, time-varying, heterogeneous, even unbounded delays are permitted. To overcome the difficulties from this kind of delay as well as diffusion effects, a comparison-based approach is applied to this model and a series of algebraic criteria are successfully obtained to verify the global asymptotical synchronization. By specifying the existing delays, some M -matrix-based criteria are derived to justify the power-rate synchronization and exponential synchronization. In addition, new criterion on synchronization of general connected neural networks without diffusion effects is also given. Finally, two simulation examples are given to verify the effectiveness of the obtained theoretical results and provide a comparison with the existing criterion.

This paper considers the tracking synchronization problem for a class of coupled reaction-diffusion neural networks (CRDNNs) with undirected topology. For the case where the tracking trajectory has identical individual dynamic as that of the network nodes, the edge-based and vertex-based adaptive strategies on coupling strengths as well as adaptive controllers, which demand merely the local neighbor information, are proposed to synchronize the CRDNNs to the tracking trajectory. To reduce the control costs, an adaptive pinning control technique is employed. For the case where the tracking trajectory has different individual dynamic from that of the network nodes, the vertex-based adaptive strategy is proposed to drive the synchronization error to a relatively small area, which is adjustable according to the parameters of the adaptive strategy. This kind of adaptive design can enhance the robustness of the network against the external disturbance posed on the tracking trajectory. The obtained theoretical results are verified by two representative examples.

In this paper, stabilization for a class of Takagi-Sugeno (T-S) fuzzy memristive neural networks (FMNNs) with mixed time delays is investigated. By virtue of theories of differential equations with discontinuous right-hand sides, inequality techniques, and the comparison method, an algebraic criterion is derived to stabilize the addressed FMNNs with bounded discrete and distributed time delays via a designed fuzzy state feedback controller in Filippov's sense. The result can be reinforced to stabilize FMNNs with unbounded discrete time delays. Meanwhile, exponential stabilization of FMNNs with bounded discrete time delays and unbounded continuously distributed delays is also discussed. FMNNs in this study are general since fuzzy logics and hybrid time delays are all considered, and the obtained conditions enhance and extend some existing ones. Finally, four numerical simulations are carried out to substantiate the efficiency and merits of developed theoretical results.

This paper investigates the synchronization issue of coupled reaction-diffusion neural networks with directed topology via an adaptive approach. Due to the complexity of the network structure and the presence of space variables, it is difficult to design proper adaptive strategies on coupling weights to accomplish the synchronous goal. Under the assumptions of two kinds of special network structures, that is, directed spanning path and directed spanning tree, some novel edge-based adaptive laws, which utilized the local information of node dynamics fully are designed on the coupling weights for reaching synchronization. By constructing appropriate energy function, and utilizing some analytical techniques, several sufficient conditions are given. Finally, some simulation examples are given to verify the effectiveness of the obtained theoretical results.

This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.