In this article, we investigate a class of differential games with impulsive effects, where Player 1 employs piecewise continuous control, and Player 2 utilizes event-triggered impulses. Exploiting the dual nature of impulsive actions, we develop tailored event-triggering mechanisms (ETMs) for both control inputs and disturbances. To reflect practical limitations, we assume that some system states are unmeasurable. Building on this framework, we establish a critical connection between system stability and the existence of equilibrium solutions. This relationship guarantees the presence of saddle points or Nash equilibria while simultaneously enabling stability analysis. Finally, two numerical examples are provided to demonstrate the validity of our theoretical findings.

In this article, the memristor-based selective convolutional (MSC) circuit for salt-and-pepper (SAP) noise removal was proposed. In experiments, the MSC model was built and benchmarked against a ternary selective convolutional (TSC) model. Results show that the MSC model effectively restores images corrupted by SAP noise, achieving similar performance to the TSC model in both quantitative measures and visual quality at noise densities of up to 50%. In addition, this study proposes an enhanced MSC (MSCE) model based on MSC, which reduces power consumption by 57.6% compared with the MSC model while improving performance. The MSCE model maintains reliability when memristors experience conductance drift rates of less than 30% and yields greater than 89%.

Location-based mobile services, while improving user daily life, also raise significant privacy concerns in the sharing of location data. These trajectories indicate users’ traveling behavioural traces with rich semantics derived from open-source information. Behavioral-semantic analysis reveals users’ travelling motivations and underlying behavioral patterns. It contributes to attackers launching inferential attacks for behavior prediction, identity identification, or other privacy invasions, even when the location data is protected. It remains open to the issues of behavioral-semantic privacy-risk quantification and privacy-protection evaluation. This paper aims to reveal such semantic privacy risks of user behaviors arising from the publication of location trajectories in mobile scenarios. We formalize user semantic-mobility process to analyze his underlying behavior patterns. Then, we design semantic inference algorithms conditional on the released trajectory to reason about the observation-based likelihood of the user’s actual staying and transfer behaviours and behavioural-trace tracking. Extensive experiments with real-world data demonstrate their performance on inference accuracy and semantic similarity, offering a quantification criterion for deploying mobile privacy protection.

This article presents a novel proximal gradient neurodynamic network (PGNN) for solving composite optimization problems (COPs). The proposed PGNN with time-varying coefficients can be flexibly chosen to accelerate the network convergence. Based on PGNN and sliding mode control technique, the proposed time-varying fixed-time proximal gradient neurodynamic network (TVFxPGNN) has fixed-time stability and a settling time independent of the initial value. It is further shown that fixed-time convergence can be achieved by relaxing the strict convexity condition via the Polyak-Lojasiewicz condition. In addition, the proposed TVFxPGNN is being applied to solve the sparse optimization problems with the log-sum function. Furthermore, the field-programmable gate array (FPGA) circuit framework for time-varying fixed-time PGNN is implemented, and the practicality of the proposed FPGA circuit is verified through an example simulation in Vivado 2019.1. Simulation and signal recovery experimental results demonstrate the effectiveness and superiority of the proposed PGNN.

In this article, several novel time-varying momentum-like neurodynamic optimization approaches are proposed for Nash equilibrium (NE) seeking of noncooperative games. It is shown that the dynamics trajectories converge to NE within fixed-time from arbitrary initial conditions, achieving a quicker convergence rate through the selection of distinct time-varying coefficients. Moreover, the upper bounds of the settling time for the proposed NE seeking neurodynamic approaches are explicitly provided. In addition, the study investigates the robustness of the designed neurodynamic approaches in the presence of bounded noises. The superior convergence properties and practicability of our approaches are demonstrated through a simulation example involving energy consumption games.

Crowdsensing-based mobile Internet, while facilitating users’ daily life, also raises privacy concerns because of sharing user location trajectories. Combining with open-source network information, these trajectories reveal the semantics of users’ social behaviors in their travels, thus indicating their behavioral traces. Based on such social mobilities, attackers can explore users’ potential behavioral patterns and launch powerful behavioral-semantic inferential attacks for behavior prediction, identity identification, and threatening users’ location-related mobile privacy. Even through privacy protection, the released similar anonymous semantics may still bring significant privacy gains to such attacks. To the best of our knowledge, there is still no effective technique to counter such attacks and protect user behavioral semantics in mobile Internet services. To this end, this article proposes a posterior behavioral-semantic privacy-preserving solution, BSPri, by simulating the inferential attacks to eliminate the privacy risks associated with released traces. Specifically, we represent the logical association between semantic attributes and propose a similar semantic clustering and ranking method. Then, we formalize the user social-mobility stochastic process to characterize the privacy risks arising from the attacker’s observation of the released trajectory, and define a observation-based posterior privacy authentication criteria to filter anonymous semantics further. Finally, we generate synthetic trajectories with similar anonymity semantics, which bring attackers insignificant privacy gain, for users to participate in applications. Extensive experiments with the real-world data set demonstrate that our BSPri achieves an effective privacy-preserving performance, i.e., rigorous posterior-privacy constraint with limited data-availability loss, such as, distance 752 m$(47$-m closer, compared with our previous work MSP), direction deviation$39.5^{\circ }~(11.5^{\circ }$smaller), and semantic similarity$43.4\%~(8.4\%$closer).

While facilitating user daily lives, the booming development of mobile Internet services raises their privacy concerns because of the need to share travel trajectories. Due to the differences in access patterns and sensitive location attributes, behavioral semantics of user travel suffer from different degrees of leakage risks and have personalized privacy requirements. Semantic mobility-aware personalized privacy protection is still an open research issue in mobile scenarios. To this end, we propose a differentially semantic-generalized behavioral trajectory (DSG-BTra) for achieving privacy-preserving mobile Internet services. Specifically, we first explore the underlying behavioral patterns by formalizing user social mobility. Then, we evaluate the differential privacy sensitivity of user behavior to indicate the risks it faces. Finally, we generalize the behavioral semantics with a sensitivity-quantified strength and generate a DSG-BTra for the user to participate in mobile services. Extensive experiments with real-world data sets demonstrate DSG-BTra achieves flexible balance between privacy protection and application QoS, e.g., reducing the inference probability to 0.18–0.26 with a semantic similarity of 0.3–0.5.

The novel IoT-based data sensing and service mode promotes the booming development of crowdsensing-based mobile communication services (MCSs). MCS facilitates people’s daily lives by providing appropriate services according to the user’s mobile travels. These traveling trajectories, combined with open-source network information, reveal multimodal semantic information implicit in user mobility. Mining these mobile semantics contributes to understanding user mobility more sufficiently. It covers a wide spectrum of applications in mobile scenarios. For service providers, it improves the quality of their services. For mobile users, it helps to design a more rigorous privacy-preserving mechanism. For third-party platforms, such mobility analysis enhances their data management, analysis, and reusage. It has always been an open research issue in mobile computing. We are motivated to conduct a complete and comprehensive survey on semantic mining within the scope of MCS, forming a complete overview of mobile semantic perception. Specifically, we first review existing research works on feature selection. We classify them into five categories, depending on their representation forms. Then, we summarize the research on mobile semantic perception and cluster them to be three groups according to the digging depth of the represented semantics. To complete the overview, we also review the applications of learning algorithms and discuss the open opportunities and challenges for future works.

The current investigation explores the leader-following consensus problem for nonlinear multiagent systems under the output feedback control mechanism and the event-triggered communication mechanism. Owing to the physical instrument constraints, a significant portion of the state variables is not readily available. Therefore, this article put forward a distributed event-based leader-following consensus protocol only using agents' relative output measurements and underlying neighbors. Furthermore, this article develops two event-triggered mechanisms simultaneously, one is the event-triggered communication mechanism in the sensor-to-controller channel, and another is the event-triggered controller update in the controller-to-actuator track. Besides that, it is proven that the developed event-triggered control protocol can settle the leader-following consensus problem of the nonlinear multiagent systems, and the Zeno behavior is excluded in both the channels. Finally, we perform two simulation examples to illustrate the efficacy of the obtained results.

In this article, we address the synchronization issue for coupled neural networks (CNNs) with mixed couplings by way of the delayed impulsive control, where the delay is distributed. Particularly, mixed couplings comprise the current-state coupling and the distributed-delay coupling, where influences on network connections caused by the past information of CNNs over a certain period are considered. First, we propose a novel array of delayed impulsive differential inequalities involving distributed-delay-dependent impulses, where distributed delays can be relatively larger. Second, we apply such delayed inequalities to analyze the problem of synchronization for CNNs with two different topologies. Sufficient criteria and distributed-delay-dependent impulsive controller are derived thereby. Furthermore, using techniques of matrix decomposition, several low-dimensional criteria are set out, which are appropriate for applications of large scale CNNs. Finally, a numerical example of CNNs with both the current-state coupling and the distributed-delay coupling involving three cases, are exhibited to exemplify the validity and the efficiency of the obtained theoretical results.

This article proposes a novel fixed-time converging proximal neurodynamic network (FXPNN) via a proximal operator to deal with equilibrium problems (EPs). A distinctive feature of the proposed FXPNN is its better transient performance in comparison to most existing proximal neurodynamic networks. It is shown that the FXPNN converges to the solution of the corresponding EP in fixed-time under some mild conditions. It is also shown that the settling time of the FXPNN is independent of initial conditions and the fixed-time interval can be prescribed, unlike existing results with asymptotical or exponential convergence. Moreover, the proposed FXPNN is applied to solve composition optimization problems (COPs),$l_{1}$-regularized least-squares problems, mixed variational inequalities (MVIs), and variational inequalities (VIs). It is further shown, in the case of solving COPs, that the fixed-time convergence can be established via the Polyak–Lojasiewicz condition, which is a relaxation of the more demanding convexity condition. Finally, numerical examples are presented to validate the effectiveness and advantages of the proposed neurodynamic network.

This article investigates the issue of synchronization for a type of uncertain coupled neural networks (CNNs) involving time-varying delay with unmeasured or unknown bound by delayed impulsive control with distributed delay. A new Halanay-like delayed differential inequality is presented, and both cases of impulsive control and impulsive perturbation are well-considered. Stemmed from this new inequality and techniques of linear matrix inequalities (LMIs), some sufficient criteria are obtained to achieve both dynamically and statically global μ -synchronization of the delayed CNNs, and a distributed-delay-dependent impulsive controller is designed. A numerical simulation is provided to demonstrate the validity of the obtained theoretical results.

In this article, we propose a novel class of mathematical models of uncertain switched nonlinear systems with saturation constraints on both the sampled-data control signal and the impulsive signal, which can reflect the actuator saturation phenomenon of hybrid control signals more realistically. Based on the Lyapunov stability theory, polytopic representation approach, matrix inequality, and Schur complement, we analyze the robust stability of the considered system, overcoming the relevant difficulties from the parameter uncertainty, the discontinuity produced by impulsive effect and the input constraints on both the sampled-data control signal and the impulsive signal. Moreover, to make it easier to find the suitable control gains, the design of the hybrid control gains is investigated. And, some optimization problems are also established to obtain the larger estimation of the attraction domain. Simulation results for the system consisting of two neural network subsystems are presented to show the feasibility and effectiveness of our robust stabilization methods and the LMI optimization problems.

This article proposes a novel fixed-time converging forward-backward-forward neurodynamic network (FXFNN) to deal with mixed variational inequalities (MVIs). A distinctive feature of the FXFNN is its fast and fixed-time convergence, in contrast to conventional forward-backward-forward neurodynamic network and projected neurodynamic network. It is shown that the solution of the proposed FXFNN exists uniquely and converges to the unique solution of the corresponding MVIs in fixed time under some mild conditions. It is also shown that the fixed-time convergence result obtained for the FXFNN is independent of initial conditions, unlike most of the existing asymptotical and exponential convergence results. Furthermore, the proposed FXFNN is applied in solving sparse recovery problems, variational inequalities, nonlinear complementarity problems, and min-max problems. Finally, numerical and experimental examples are presented to validate the effectiveness of the proposed neurodynamic network.

We study how to achieve the state consensus of a whole multi-agent system after adding some new agent groups dynamically in the original multi-agent system. We analyze the feasibility of dynamically adding agent groups under different forms of network topologies that are currently common, and obtain four feasible schemes in theory, including one scheme that is the best in actual industrial production. Then, we carry out dynamic modeling of multi-agent systems for the best scheme. Impulsive control theory and Lyapunov stability theory are used to analyze the conditions so that the whole multi-agent system with dynamic join characteristics can achieve state consensus. Finally, we provide a numerical example to verify the practicality and validity of the theory.

In this article, the consensus problem of nonlinear multiagent systems with grouping via state-constraint impulsive protocols is investigated. Two types of cases with and without leader agent are studied by using two kinds of protocols. A judgement strategy is designed to decide to group in the nonlinear multiagent systems, and two kinds of state-constraint impulsive control protocols, which include partial state constraint and full state constraint, are proposed to make this system cut down the cost of communication and reduce irreversible damage to equipment. Then, based on the algebraic graph theory, the Lyapunov stability theory, and the matrix theory, some sufficient conditions are established to deal with the consensus problem in the nonlinear multiagent systems. The presented results can be used to solve the consensus problem in the nonlinear multiagent systems with grouping. Finally, some important simulations are presented to illustrate the feasibility of the theoretical results.

An observer-based dissipativity control for Takagi-Sugeno (T-S) fuzzy neural networks with distributed time-varying delays is studied in this article. First, the network channel delays are modeled as a distributed delay with its kernel. To make full use of kernels of the distributed delay, a Lyapunov-Krasovskii functional (LKF) is established with the kernel of the distributed delay. It is noted that the novel LKF and delay-dependent reciprocally convex inequality plays an important role in dealing with global asymptotical stability and strict (Q, S,R) - α -dissipativity of the T-S fuzzy delayed model. Through the constructed LKF, a new set of less conservative linear matrix inequality (LMI) conditions is presented to obtain an observer-based controller for the T-S fuzzy delayed model. This proposed observer-based controller ensures that the state of the closed-loop system is globally asymptotically stable and strictly (Q, S,R) - α -dissipative. Finally, the effectiveness of the proposed results is shown in numerical simulations.

The article considers the impulsive synchronization for inertial neural networks with unbounded delay and actuator saturation via sampled-data control. Based on an impulsive differential inequality, the difficulties caused by unbounded delay and impulsive effect may be effectively avoid. By applying polytopic representation technique, the actuator saturation term is first considered into the design of impulsive controller, and less conservative linear matrix inequality (LMI) criteria that guarantee asymptotical synchronization for the considered model via hybrid control are given. As special cases, the asymptotical synchronization of the considered model via sampled-data control and saturating impulsive control are also studied, respectively. Numerical simulations are presented to claim the effectiveness of theoretical analysis. A new image encryption algorithm is proposed to utilize the synchronization theory of hybrid control. The validity of image encryption algorithm can be obtained by experiments.

The impulsive stabilization of nonlinear time-delay system with input saturation via delay-dependent polytopic approach is studied in this article. Different from polytopic representation technique, delay-dependent polytopic technique is able to estimate a larger domain of attraction. Based on this approach, the actuator saturation term is first introduced into the design of impulsive controller, which is expressed as a convex combination of the product of delay-dependent state vectors and auxiliary matrices. By applying delay-dependent polytopic technique and delay-dependent Lyapunov–Krasovskii functional (LKF) approach, a new series of less conservative linear matrix inequality (LMI) criteria are obtained to ensure the stability of the established model. Finally, two examples are presented to claim the effectiveness of theoretical analysis results.

Energy constrains are always significant to be considered in control of multiagent systems. Besides, nonlinear phenomena are often involved into such systems. In this paper, we discuss the impulsive consensus problem of nonlinear multiagent systems via impulsive protocol with limited bandwidth communication based on encoding-decoding. The scheme based on encoding-decoding with impulsive protocol is introduced to multiagent systems in general directed networks topology of which the graph is strongly connected. The impulsive protocols and limited bandwidth communication enhance the performance on energy saving and the involvement of nonlinear dynamics could suit more real-world cases. The design of encoders and decoders is presented, which is the key to achieve the goal that the information exchanged is subject to limited bandwidth communication. The conditions to guarantee the impulsive consensus and the conditions to avoid quantizer saturation are obtained. Moreover, the convergence rate of such multiagent systems are also characterized by the analysis of the exponential consensus. The numerical simulations are presented to support the theoretical results.

This paper presents the impulsive average quasi-consensus algorithm for distributed constrained convex optimization. First, the constrained optimization problem can be transformed into an unconstrained problem using the interior point method, and then a distributed algorithm is modeled by means of impulsive differential equation. In the framework of the continuous-time gradient method and algebraic graph theory, each agent can deal with one local objective function with local constraints. At the impulsive instants, each agent can communicate with its neighboring agents over the network. Under certain conditions, the impulsive average quasi-consensus is achieved. It is shown that the state of average quasi-consensus is the optimal solution of the aforementioned unconstrained optimization problem, and the state of each agent can also reach the neighborhood of the optimal solution. Finally, two numerical examples show the effectiveness of the proposed impulsive average quasi-consensus algorithm. Moreover, the feasibility of the approach is verified by an application to one sensor network localization problem.

In this paper, we mainly investigate two kinds of consensuses of multi-agent systems (MASs) with nonlinear dynamics based on impulsive control, event-triggered control, and sampled-data control. The two types of impulsive protocols are proposed for the case without and with leader agent. Edge event-triggered technique is presented, where for each communication link, occurrence of edge event can activate the mutual state sampling and controller update of the corresponding agents. The control approach combines the characteristics of impulsive control and edge event-triggered control and is defined as "impulsive edge event-triggered control." It has good performance in robustness against disturbance and reduces the communication cost. The results with the aid of the Lyapunov function approach and stability theory of impulsive control show that if some sufficient conditions are satisfied, the consensus of MASs can be guaranteed and the rate of convergence can be exponentially estimated. Additionally, Zeno-behavior can be eliminated by using impulsive edge event-triggered control, which reduces the burden of event detectors. Finally, two simulations are provided to illustrate the effectiveness and performance of our theoretical analysis.

This paper is concerned with the consensus issue for a class of multiagent systems with Markovian switching topology under aperiodic sampled data measurements. By constructing a novel piecewise stochastic Lyapunov-Krasovskii functional, some novel conditions with less conservative are established such that the consensus is achieved in the mean square sense. In contrast to some previous publications, the sample period is no longer fixed and the transition probability matrix of Markovian switching topology is uncertain. This issue which is of practical and theoretical significance is further investigated when the sampled data controller of each agent is suffered from distinct time-varying input delay. Quite different with the related studies, a maximally allowable input delay upper bound is replaced by the permissible input delay interval. Furthermore, the corresponding consensus is elegantly obtained in terms of linear matrix inequalities. Finally, the effectiveness and practicability of our consensus criteria are well illustrated by the numerical examples.

Summary This paper is concerned with a tracking control problem of multi‐agent systems with noises. It is assumed that each agent in the network updates its state only at some discrete time instants, which determined by the event‐triggered condition, and the agents are affected by noises. In order to attenuate the effect of noises, consensus‐gain function is introduced in the control protocol. Centralized and decentralized event‐triggered protocols are proposed to ensure that the followers track the considered leader. With the help of matrix theory and Lyapunov method, sufficient conditions are derived to solve the mean square tracking control. Simulation results are provided to illustrate the theoretical results.

This paper investigates the fixed-time synchronization (FDTS) of complex networks with stochastic perturbations. A new control scheme is designed to realize the synchronization goal. Moreover, the designed controller without sign function is continuous, which means the chattering phenomenon in some previous results can be avoided. By constructing Lyapunov functionals, using the properties of the Weiner process as well as applying a designed comparison system, several FDTS criteria are obtained. Synchronization criteria of this paper are very general and can be utilized in directed and undirected weighted networks. Numerical simulations are given to illustrate the theoretical results.

This paper focuses on the problem of the exponential synchronizationlike criteria for state-dependent impulsive dynamical networks (SIDNs). Two types of sufficient conditions, which are applied to ensure every solution intersecting each impulsive surface exactly once, are derived. For each type of collision conditions, combining with comparison principle and inequality techniques, some sufficient conditions are obtained to ensure local exponential synchronizationlike for SIDN. Moreover, a quiet different impulsive strategy concerning the trigger rules of impulsive instants is proposed. Finally, an example is given to demonstrate the effectiveness of our results.

This paper addresses the state-dependent impulsive effects on robust exponential stability of quaternion-valued neural networks (QVNNs) with parametric uncertainties. In view of the noncommutativity of quaternion multiplication, we have to separate the concerned quaternion-valued models into four real-valued parts. Then, several assumptions ensuring every solution of the separated state-dependent impulsive neural networks intersects each of the discontinuous surface exactly once are proposed. In the meantime, by applying the B -equivalent method, the addressed state-dependent impulsive models are reduced to fixed-time ones, and the latter can be regarded as the comparative systems of the former. For the subsequent analysis, we proposed a novel norm inequality of block matrix, which can be utilized to analyze the same stability properties of the separated state-dependent impulsive models and the reduced ones efficaciously. Afterward, several sufficient conditions are well presented to guarantee the robust exponential stability of the origin of the considered models; it is worth mentioning that two cases of addressed models are analyzed concretely, that is, models with exponential stable continuous subsystems and destabilizing impulses, and models with unstable continuous subsystems and stabilizing impulses. In addition, an application case corresponding to the stability problem of models with unstable continuous subsystems and stabilizing impulses for state-dependent impulse control to robust exponential synchronization of QVNNs is considered summarily. Finally, some numerical examples are proffered to illustrate the effectiveness and correctness of the obtained results.

The problem of asynchronous dissipative control is investigated for Takagi-Sugeno fuzzy systems with Markov jump in this paper. Hidden Markov model is introduced to represent the nonsynchronization between the designed controller and the original system. By the fuzzy-basis-dependent and mode-dependent Lyapunov function, a sufficient condition is achieved such that the resulting closed-loop system is stochastically stable with a strictly ( , , )- -dissipative performance. The controller parameter is derived by applying MATLAB to solve a set of linear matrix inequalities. Finally, we present two examples to confirm the validity and correctness of our developed approach.

This paper investigates the problem of finite-time drive-response synchronization for a class of neural networks with discontinuous activations, time-varying discrete and infinite-time distributed delays, and mismatched parameters. In order to cope with the difficulties induced by discontinuous activations, time delays, as well as mismatched parameters simultaneously, new 1-norm-based analytical techniques are developed. Both state feedback and adaptive controllers with and without the sign function are designed. Based on differential inclusion theory and Lyapunov functional method, several sufficient conditions on the finite-time synchronization are obtained. Our results show that the controllers with a sign function can reduce the conservativeness of control gains and the controllers without a sign function can overcome the chattering phenomenon. Numerical examples are given to show the effectiveness of the theoretical analysis.

This letter discusses behaviors of multi-dimensional memristor models. A second dimensional memristor model is extracted from the third dimensional memristor model. Parameters of this memristor model are physically defined and analyzed. A comparison between the first, the second and the third dimensional models is taken. The effect of the diffusion term on five typical window functions is analyzed. Besides, we provide a visual interface to exhibit these memristor properties.

Recently, projection neural network (PNN) was proposed for solving monotone variational inequalities (VIs) and related convex optimization problems. In this paper, considering the inertial term into first order PNNs, an inertial PNN (IPNN) is also proposed for solving VIs. Under certain conditions, the IPNN is proved to be stable, and can be applied to solve a broader class of constrained optimization problems related to VIs. Compared with existing neural networks (NNs), the presence of the inertial term allows us to overcome some drawbacks of many NNs, which are constructed based on the steepest descent method, and this model is more convenient for exploring different Karush-Kuhn-Tucker optimal solution for nonconvex optimization problems. Finally, simulation results on three numerical examples show the effectiveness and performance of the proposed NN.

In this brief, hybrid impulsive and adaptive feedback controllers are simultaneously exerted on a general delayed memristive neural network (MNN) model to formulate a novel impulsive controlled MNN (IMNN) model with variable delays. By means of Lyapunov-Razumikhin technique and other analytical ways, several new stability criteria of the proposed IMNN model are obtained. In addition, by choosing appropriate impulses and external inputs, the convergence speed of IMNN can be increased, which implies that its dynamic behaviors will be optimized. Finally, the effectiveness of the obtained results is illustrated by one numerical example.

In this brief, we establish a novel complex-valued memristive recurrent neural network (CVMRNN) to study its stability. As a generalization of real-valued memristive neural networks, CVMRNN can be separated into real and imaginary parts. By means of M -matrix and Lyapunov function, the existence, uniqueness, and exponential stability of the equilibrium point for CVMRNNs are investigated, and sufficient conditions are presented. Finally, the effectiveness of obtained results is illustrated by two numerical examples.

This letter uses image overlay technique on memristor crossbar array (MCA) structure for image storing. Different programming circuits with time slot techniques are designed for the MCA consisting of the nonlinear HP memristor (HPMCA) and the MCA composed of the piece-wise linear threshold memristor (TMCA). The experiment results indicate that the HPMCA has a better performance, the TMCA is more practical in the industrial implementation. As a conclusion, the MCA made up of the memristor with both the nonlinear drift boundary property and the threshold property is preferred for image overlay.

Indeed, countermeasures, as well as computer viruses, could spread in the network. This paper aims to investigate the effect of propagation of countermeasures on viral spread. For the purpose, a new virus-antivirus spreading model is proposed. The global asymptotic stability of the virus-free equilibrium is proved when the threshold is below the unity, and the existence of the viral equilibrium is shown when the threshold exceeds the unity. The influences of different model parameters on the threshold are also analyzed. Numerical simulations imply that the propagation of countermeasures contributes to the suppress of viruses, which is consistent with the fact.

Synchronization of an array of linearly coupled memristor-based recurrent neural networks with impulses and time-varying delays is investigated in this brief. Based on the Lyapunov function method, an extended Halanay differential inequality and a new delay impulsive differential inequality, some sufficient conditions are derived, which depend on impulsive and coupling delays to guarantee the exponential synchronization of the memristor-based recurrent neural networks. Impulses with and without delay and time-varying delay are considered for modeling the coupled neural networks simultaneously, which renders more practical significance of our current research. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.

Spike-timing-dependent plasticity (STDP) learning ability has been observed in physical memristors, but whether the STDP is caused by the neuron or the memristor is unclear. In this paper, we proved the STDP property in the model for both symmetric and asymmetric memristor. We also employed the symmetric/asymmetric memristors with STDP property and the simplified neurons to perform the STDP learning ability. At last, the sequence learning experiment of the memritive neural network (MNN) with the symmetric memristor synapse further verifies the STDP learning ability of the memristor.

This paper formulates and studies a more general model of coupled switched neural networks with impulsive time window. The main feature of impulsive time window is that impulses can exist the stochastic instants of the whole switching interval not the switching instants and a pre-specified instants. Moreover, the impulsive numbers of every subsystems is not the same. Using switching Lyapunov functions and a generalized Halany inequality, some general criteria which characterize the impulses and switching effects in aggregated form, for asymptotically synchronization and exponential synchronization of this general model are established.

In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.

The future behavior of a dynamical system is determined by its initial state or initial function. Nontrivial neuron system involving adaptive learning corresponds to the memorization of initial information. In this paper, exponential estimates and sufficient conditions for the exponential stability of a single neuron system of neutral-type are studied. Of particular importance is the fact that exponential convergence guarantees that this system is capable of memorizing initial functions. Furthermore, this system is also capable of conveying much more information with respect to the initial functions memorized by neuron system with time delay. The proofs follow some new results on nonhomogeneous difference equations evolving in continuous-time combined with the Lyapunov-Krasovskii functional and the descriptor system approach. The exponential stability conditions are expressed in terms of a linear matrix inequality, which lead to less restrictive and less conservative exponential estimates.

This brief reports a retarded functional differential equation modeling tri-neuron network with time delay. The Bogdanov-Takens (B-T) bifurcation is investigated by using the center manifold reduction and the normal form method. We get the versal unfolding of the norm forms at the B-T singularity and show that the model can exhibit pitchfork, Hopf, homoclinic, and double-limit cycles bifurcations. Some numerical simulations are given to support the analytic results and explore chaotic dynamics. Finally, an algorithm is given to show that chaotic tri-neuron networks can be used for encrypting a color image.

This article addresses an iterative learning control (ILC) design for a class of linear discrete-time systems with multiple time delays. In order to improve the tracking performance, we introduce a P-type high-order iterative learning algorithm that makes use of information from several previous iterations. An initial state learning scheme is proposed to eliminate the effect of the initialization error on the final tracking error. Furthermore, we establish a sufficient condition to ensure asymptotic convergence. A simulation example is also provided to illustrate the effectiveness of the proposed result.

This paper focuses on the hybrid effects of parameter uncertainty, stochastic perturbation, and impulses on global stability of delayed neural networks. By using the Ito formula, Lyapunov function, and Halanay inequality, we established several mean-square stability criteria from which we can estimate the feasible bounds of impulses, provided that parameter uncertainty and stochastic perturbations are well-constrained. Moreover, the present method can also be applied to general differential systems with stochastic perturbation and impulses.

This brief studies the global exponential stability of the equilibrium point of discrete-time delayed Hopfield neural networks (DHNNs) with impulse effects by using difference inequalities. We shall consider the stabilizing effects of impulses when the corresponding impulse-free DHNN is even not asymptotically stable. The obtained results characterize the aggregated effects of impulses and deviation of the impulse-free DHNN from its equilibrium point on the exponential stability of the whole system. It is shown that, because of effects of impulses, the impulsive discrete-time DHNN may be exponentially stable even if the evolution of impulse-free component deviates from its equilibrium point exponentially.

This paper further studies the exponential stability of delayed bidirectional associative memory neural networks and focuses on the impulse effect on the exponential stability property. It is shown that if the corresponding impulse-free DBAM is globally exponentially stable the impulsive analog will remain its stability property even if the measurements of the states are magnified to some extent at the impulse instants. Furthermore, the admissible upper bound of impulse is estimated in terms of exponential convergence degree of the corresponding impulse-free DBAM and the length of impulse interval.

This paper formulates and studies a model of hybrid impulsive and switching Hopfield neural networks (NNs). Using switching Lyapunov functions and a generalized Halanay inequality, some general criteria, which characterize the impulse and switching effects in aggregated form, for asymptotic and exponential stability of such NNs with arbitrary and conditioned impulsive switching are established. Several numerical examples are given for illustration and interpretation of the theoretical results.