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This paper focuses on the study of synchronization problem for T-S fuzzy memristive neural networks with time delay. First, a delay-independent nonlinear fuzzy control is designed. Second, under the designed fuzzy control, two kinds of finite-time synchronization criteria are obtained by comparison method and Lyapunov function method, respectively. Furthermore, the settling time is estimated. Finally, a numerical simulation example is provided to demonstrate the effectiveness and feasibility of the theoretical results, and an application of the obtained theories is also given in the pseudorandom number generator (PRNG). [ABSTRACT FROM AUTHOR]

This paper presents theoretical results on multiple asymptotical ω -periodicity of a state-dependent switching fractional-order neural network with time delays and sigmoidal activation functions. Firstly, by combining the geometrical properties of activation functions with the range of switching threshold, a partition of state space is given. Then, the conditions guaranteeing that the solutions can approach each other infinitely in each positive invariant set are derived. Furthermore, the S -asymptotical ω -periodicity and the convergence of solutions in positive invariant sets are discussed. It is worth noting that the number of attractors increases to 3 n from 2 n in a neural network without switching. Finally, three numerical examples are given to substantiate the theoretical results. • Proposed a switched fractional-order neural network model. • Proved the S-asymptotical ω -periodicity of solutions. • Investigated the multiple asymptotical ω -periodicity of switching system. [ABSTRACT FROM AUTHOR]

In this paper, we address the finite-time and fixed-time synchronization of a general class of switched neural networks (SNNs) with time delays subject to stochastic disturbances. Considering two types of switching in this class of SNNs: 1) intra-SNN state-dependent switching and 2) inter-SNN Markovian switching, we develop three control laws and derive three sets of sufficient conditions for both finite-time and fixed-time synchronization of SNNs subject to stochastic disturbances. We make two remarks on the effects of control-law parameters on synchronization settling time. Moreover, we derive several upper bounds of synchronization settling time and evaluate their pros and cons. Finally, we elaborate on two numerical examples to illustrate the viability of the theoretical results. [ABSTRACT FROM AUTHOR]

• Introduce the saturated treatment rate into the network-based epidemic model with saturated incidence rate. • Analyze the boundedness of solutions, the basic reproduction number R0, the existence and stability of equilibrium points. • Study the backward bifurcation due to the introduction of saturated treatment. • Analyze an optimal control problem with consideration of two time-dependent control measures. In this paper, to characterize the limited availability of medical resources, we incorporate a saturated treatment rate into a network-based susceptible-infected-susceptible (SIS) epidemic model with time delay and nonlinear incidence rate. Analytical study shows the boundedness of solutions, the basic reproduction number R 0 and equilibrium points of the proposed system. For any infection delay, we perform both local and global stability analyses for the disease-free equilibrium point by analyzing the characteristic equation and using Lyapunov functional. Furthermore, this system exhibits bifurcation behavior at R 0 = 1 due to the introduction of saturated treatment. More precisely, a backward bifurcation takes place from the disease-free equilibrium point when the saturation constant β is sufficiently large. Under the given conditions, the unique disease-spreading equilibrium point is also proved to be locally asymptotically stable. In addition, we analyze an optimal control problem with consideration of two time-dependent control measures. Several numerical simulations are presented to validate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents new theoretical results on the multi-periodicity of recurrent neural networks with time delays evoked by periodic inputs under stochastic disturbances and state-dependent switching. Based on the geometric properties of activation function and switching threshold, the neuronal state space is partitioned into 5 n regions in which 3 n ones are shown to be positively invariant with probability one. Furthermore, by using Itô's formula, Lyapunov functional method, and the contraction mapping theorem, two criteria are proposed to ascertain the existence and mean-square exponential stability of a periodic orbit in every positive invariant set. As a result, the number of mean-square exponentially stable periodic orbits increases to 3 n from 2 n in a neural network without switching. Two illustrative examples are elaborated to substantiate the efficacy and characteristics of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents new theoretical results on the multistability of switched recurrent neural networks with radial basis functions and state-dependent switching. By partitioning state space, applying Brouwer fixed-point theorem and constructing a Lyapunov function, the number of the equilibria and their locations are estimated and their stability/instability are analyzed under some reasonable assumptions on the decomposition of index set and switching threshold. It is shown that the switching threshold plays an important role in increasing the number of stable equilibria and different multistability results can be obtained under different ranges of switching threshold. The results suggest that switched recurrent neural networks would be superior to conventional ones in terms of increased storage capacity when used as associative memories. Two examples are discussed in detail to substantiate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper focuses on the global exponential synchronization of multiple memristive reaction–diffusion neural networks (MRDNNs) with time delay. Due to introducing the influences of space as well as time on state variables and replacing resistors with memristors in circuit realization, the state-dependent partial differential mathematical model of MRDNN is more general and realistic than traditional neural network model. Based on Lyapunov functional theory, Divergence theorem and inequality techniques, global exponential synchronization criteria of coupled delayed MRDNNs are derived via directed and undirected nonlinear coupling. Finally, three numerical simulation examples are presented to verify the feasibility of our main results. [ABSTRACT FROM AUTHOR]

This paper presents theoretical results on the multistability of switched neural networks with commonly used sigmoidal activation functions under state-dependent switching. The multistability analysis with such an activation function is difficult because state–space partition is not as straightforward as that with piecewise-linear activations. Sufficient conditions are derived for ascertaining the existence and stability of multiple equilibria. It is shown that the number of stable equilibria of an n -neuron switched neural networks is up to 3 n under given conditions. In contrast to existing multistability results with piecewise-linear activation functions, the results herein are also applicable to the equilibria at switching points. Four examples are discussed to substantiate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite/fixed-time synchronization (FFTS) problems of two delayed memristive reaction–diffusion neural networks (MRDNNs). By designing appropriate state feedback controllers, utilizing the Lyapunov function method and inequality techniques, several sufficient criteria are derived to guarantee the FFTS of the drive-response MRDNNs. Taking into account both the influences of time and space, the model, described as a state-dependent switching system here, is more complex and closer to practical applications than those in the existing results. Finally, an example is presented to substantiate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper concerns the synchronization problem of memristive high-order competitive neural networks with time-varying delay. First, a novel control scheme with a linear term and a discontinuous term is proposed. Then, based on the Lyapunov stability theory, several criteria with algebraic form or matrix form are derived to ensure global exponential synchronization of the networks by adopting some inequality techniques. Finally, two numerical examples are presented to substantiate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

The paper focuses on the multistability problems of the switched complex-valued neural networks with state-dependent switching rules. Based on the differential inclusions theory and fixed point theorem, several sufficient conditions are derived to ascertain that there exist 25 n equilibria, 9 n of which are locally ex for n -neuron switched complex-valued neural networks. The number of stable equilibria of an n -neuron switched complex-valued neural network increases significantly from 4 n to 9 n compared with the conventional complex-valued neural networks. Finally, four numerical examples are presented to substantiate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, global exponential synchronization of multiple coupled inertial memristive neural networks with time-varying delay is investigated. First, by choosing suitable variable substitution, the inertial memristive neural networks are transformed into first-order differential equations. Next, a novel coupling scheme with linear diffusive term and discontinuous sign function term depending on the first order derivative of state variables is introduced. Based on this coupling scheme, several sufficient conditions for global exponential synchronization of multiple inertial memristive neural networks are derived by using Lyapunov stability theory and some inequality techniques. Finally, several numerical examples are presented to substantiate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite-time synchronization problem of drive-response inertial memristive neural networks with time delay. First, by choosing suitable variable substitution, the original system can be transformed into the first order differential equations. Next, a delay-dependent controller is designed to ensure that finite-time synchronization can be achieved between drive system and response system based on finite time stability theory. Moreover, the settling time is estimated, and optimized based on the relationship between the settling time and parameter η . Finally, an example is presented to substantiate the effectiveness for those theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the theoretical analysis on exponential synchronization of a class of coupled switched neural networks suffering from stochastic disturbances and impulses is presented. A control law is developed and two sets of sufficient conditions are derived for the synchronization of coupled switched neural networks. First, for desynchronizing stochastic impulses, the synchronization of coupled switched neural networks is analyzed by Lyapunov function method, the comparison principle and a impulsive delay differential inequality. Then, for general stochastic impulses, by partitioning impulse interval and using the convex combination technique, a set of sufficient condition on the basis of linear matrix inequalities (LMIs) is derived for the synchronization of coupled switched neural networks. Eventually, two numerical examples and a practical application are elaborated to illustrate the effectiveness of the theoretical results. • Propose a switched coupled neural network which subject to stochastic disturbances and impulses. • Analyze the synchronization of switched neural network with desynchronizing stochastic impulses. • Analyze the synchronization of switched neural network with general stochastic impulses. [ABSTRACT FROM AUTHOR]

In this brief, we study a class of memristor-based recurrent neural networks (MRNNs) with time-varying delays. Easily verifiable delay-independent criteria are established to ensure the existence and global exponential stability of periodic solutions by using novel analysis techniques, which not only improve but also complement some existing ones. These theoretical results are also supported with numerical simulations. [ABSTRACT FROM AUTHOR]

This paper presents theoretical results on global exponential synchronization of multiple memristive neural networks in the presence of external noise by means of two types of distributed pinning control. The multiple memristive neural networks are coupled in a general structure via a nonlinear function, which consists of a linear diffusive term and a discontinuous sign term. A pinning impulsive control law is introduced in the coupled system to synchronize all neural networks. Sufficient conditions are derived for ascertaining global exponential synchronization in mean square. In addition, a pinning adaptive control law is developed to achieve global exponential synchronization in mean square. Both pinning control laws utilize only partial state information received from the neighborhood of the controlled neural network. Simulation results are presented to substantiate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global robust synchronization of multiple memristive neural networks (MMNNs) with nonidentical uncertain parameters. A coupling scheme is introduced, in a general topological structure described by a direct or undirect graph, with a linear diffusive term and a discontinuous sign term. First, a set of sufficient conditions are derived based on the Lyapunov stability theory for ascertaining global robust synchronization of coupled MMNNs. Second, a pinning adaptive coupling method is proposed to ensure global synchronization without knowing the bound of parameter uncertainties. Two illustrative examples are discussed to substantiate the theoretical results. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the global exponential synchronization of two memristor-based recurrent neural networks (MRNNs) with time delays via static or dynamic coupling. First, four coupling rules (i.e., static state coupling, static output coupling, dynamic state coupling, and dynamic output coupling) are designed for the exponential synchronization of drive-response pair of MRNNs. Then, several global exponential synchronization criteria are derived by constructing suitable Lyapunov–Krasovskii functionals based on the Lyapunov stability theory. Compared with existing results on synchronization of MRNNs, the conditions herein are easy to be verified. Moreover, the designed dynamic state coupling and output coupling rules have good anti-interference capacity. Finally, two illustrative examples are presented to substantiate the effectiveness and characteristics of the presented theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a systematic method for analyzing the robust stability of a class of interval neural networks with uncertain parameters and time delays. The neural networks are affected by uncertain parameters whose values are time-invariant and unknown, but bounded in given compact sets. Several new sufficient conditions for the global asymptotic/exponential robust stability of the interval delayed neural networks are derived. The results can be casted as linear matrix inequalities (LMIs), which are shown to be generalizations of some existing conditions. Compared with most existing results, the presented conditions are less conservative and easier to check. Two illustrative numerical examples are given to substantiate the effectiveness and applicability of the proposed robust stability analysis method. [Copyright &y& Elsevier]

Abstract: This paper addresses the global exponential dissipativity of memristor-based recurrent neural networks with time-varying delays. By constructing proper Lyapunov functionals and using -matrix theory and LaSalle invariant principle, the sets of global exponentially dissipativity are characterized parametrically. It is proven herein that there are equilibria for an -neuron memristor-based neural network and they are located in the derived globally attractive sets. It is also shown that memristor-based recurrent neural networks with time-varying delays are stabilizable at the origin of the state space by using a linear state feedback control law with appropriate gains. Finally, two numerical examples are discussed in detail to illustrate the characteristics of the results. [Copyright &y& Elsevier]

This paper mainly attempts to discuss lag H ∞ synchronization in multiple state or derivative coupled reaction–diffusion neural networks without and with parameter uncertainties. Firstly, we respectively propose two types of reaction–diffusion neural networks with multiple state and derivative couplings subject to parameter uncertainties. Secondly, by exploiting designed state feedback controllers, several criteria of the lag H ∞ synchronization for these two networks are developed based on Lyapunov functional and inequality techniques. Thirdly, lag H ∞ synchronization issues of these two networks are also coped with by virtue of devised adaptive control strategies. Finally, we provide two numerical examples to verify the obtained lag H ∞ synchronization criteria. [ABSTRACT FROM AUTHOR]

Abstract: Nonlinear dynamical systems described by differential equations with discontinuous right-hand side and solutions intended in Filippov sense are considered. Based on Filippov differential inclusion and a new chain rule for differentiating regular functions along Filippov solution trajectories, different kinds of stability and convergence results are presented. Moreover, we investigate the stability and convergence for the corresponding perturbation system of the discontinuous system and some new criteria are addressed. [Copyright &y& Elsevier]

Abstract: Without assuming that the neuron activations are bounded, some delay-independent criteria for interval delayed neural networks with discontinuous neuron activations are derived to guarantee global robust stability by using the generalized Lyapunov method and linear matrix inequality (LMI) technique. The obtained results improve and extend those given in earlier literature, and two numerical examples are also given to show the effectiveness of our results. [Copyright &y& Elsevier]

This paper is dedicated to solving the k -winners-take-all problem with large-scale input signals in a distributed manner. According to the decomposition of global input signals, a novel dynamical system consisting of multiple coordinated neural networks is proposed for finding the k largest inputs. In the system, each neural network is designed to tackle its available partial inputs only for a local objective k i ( k i ≤ k). Simultaneously, a consensus-based approach is adopted to coordinate multiple neural networks for achieving the global objective k. In addition, an inertial term is introduced in each neural network for regulating its transient behavior, which has the potential of accelerating the convergence. By developing a cocoercive operator, we theoretically prove that the multiple neural networks with inertial terms converge asymptotically/exponentially to the k -winners-take-all solution exactly from arbitrary initial states for whatever decomposition of inputs and objective. Furthermore, some extensions to distributed constrained k -winners-take-all are also investigated. Finally, simulation results are presented to substantiate the effectiveness of the proposed system as well as its superior performance over existing distributed networks. [ABSTRACT FROM AUTHOR]

This paper studies the exponential anti-synchronization problem of memristive delayed neural networks under the event-triggered controller. To reduce the recalculation of the control signals, two event-triggered control strategies including static and dynamic are proposed. A novel Lyapunov function is constructed to analyze the global exponential anti-synchronization problem. By analysis, we can choose the suitable parameter of the controller to realize global exponential anti-synchronization with a given convergence rate γ without wasting a lot of control resources. Moreover, under event-triggering conditions given in our theorem, we derive that the Zeno behavior will not happen. Finally, numerical examples are given to validate our theorem. [ABSTRACT FROM AUTHOR]

This paper investigates the global exponential synchronization problem of delayed memristive neural networks (MNNs) with reaction–diffusion terms. First, by utilizing the pinning control technique, two novel kinds of control methods are introduced to achieve synchronization of delayed MNNs with reaction–diffusion terms. Then, with the help of inequality techniques, pinning control technique, the drive–response concept and Lyapunov functional method, two sufficient conditions are obtained in the form of algebraic inequalities, which can be used for ensuring the exponential synchronization of the proposed delayed MNNs with reaction–diffusion terms. Moreover, the obtained results based on algebraic inequality complement and improve the previously known results. Finally, two illustrative examples are given to support the effectiveness and validity of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the synchronization problem on delayed memristive neural networks (MNNs) with leakage delay and parameters mismatch via event-triggered control. We divide MNNs with parameters mismatch into two categories for discussion. One is state-dependent and can achieve synchronization by designing a suitable controller. A novel Lyapunov functional is constructed to analyze the synchronization problem. Moreover, the triggering conditions are independent from the delay boundaries and can be static or dynamic. Another category of parameters mismatch is structure-dependent and can only achieve quasi-synchronization by appropriate controller. By using matrix measure method and generalized Halanay inequality, a quasi-synchronization criterion is established. The controllers in this paper are discrete state-dependent and can be updated under the event-based triggering condition, which is more simpler than the previous results. In the end of our paper, two illustrative examples are given to support our results. [ABSTRACT FROM AUTHOR]

The paper is concerned with the synchronization problem of inertial memristive neural networks with time-varying delay. First, by choosing a proper variable substitution, inertial memristive neural networks described by second-order differential equations can be transformed into first-order differential equations. Then, a novel controller with a linear diffusive term and discontinuous sign term is designed. By using the controller, the sufficient conditions for assuring the global exponential synchronization of the derive and response neural networks are derived based on Lyapunov stability theory and some inequality techniques. Finally, several numerical simulations are provided to substantiate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of reaction–diffusion high-order Hopfield neural networks with time-varying delays subject to the Dirichlet boundary condition in a bounded domain. Easily verifiable delay-independent criteria are established to ensure the existence of periodic mild solutions, and the global exponential stability of the periodic mild solutions is also discussed by using the exponential dissipation property of semigroup of operators. The obtained results are easy to check and they effectually complement previously known results. A numerical example is given to show the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the periodic synchronization problem for a general class of delayed neural networks (DNNs) with discontinuous neuron activation. One of the purposes is to analyze the problem of periodic orbits. To do so, we introduce new tools including inequality techniques and Kakutani’s fixed point theorem of set-valued maps to derive the existence of periodic solution. Another purpose is to design a switching state-feedback control for realizing global exponential synchronization of the drive–response network system with periodic coefficients. Unlike the previous works on periodic synchronization of neural network, both the neuron activations and controllers in this paper are allowed to be discontinuous. Moreover, owing to the occurrence of delays in neuron signal, the neural network model is described by the functional differential equation. So we introduce extended Filippov-framework to deal with the basic issues of solutions for discontinuous DNNs. Finally, two examples and simulation experiments are given to illustrate the proposed method and main results which have an important instructional significance in the design of periodic synchronized DNNs circuits involving discontinuous or switching factors. [ABSTRACT FROM AUTHOR]

This article presents a simple and intuitive solution for multilabel image classification, which achieves the competitive performance on the popular COCO and PASCAL VOC benchmarks. The main idea is to capture how humans perform this task: we recognize both labels (i.e., objects and attributes) and the correlation of labels at the same time. Here, label recognition is performed by a standard ConvNet pipeline, whereas label correlation modeling is done by projecting both labels and image features extracted by the ConvNet to a common latent vector space. Specifically, we carefully design the loss function to ensure that: 1) labels and features that co-appear frequently are close to each other in the latent space and 2) conversely, labels/features that do not appear together are far apart. This information is then combined with the original ConvNet outputs to form the final prediction. The whole model is trained end-to-end, with no additional supervised information other than the image-level supervised information. Experiments show that the proposed method consistently outperforms previous approaches on COCO and PASCAL VOC in terms of mAP, macro/micro precision, recall, and $F$ -measure. Further, our model is highly efficient at test time, with only a small number of additional weights compared to the base model for direct label recognition. [ABSTRACT FROM AUTHOR]

Abstract: Based on the tangency or non-tangency of the periodic solution to certain surface, this paper gives a set of conditions ensuring global convergence in finite time toward a unique periodic solution for Hopfield neural networks with discontinuous activations. Moreover, two numerical examples are provided to illustrate the theoretical results. [Copyright &y& Elsevier]