Lag Synchronization of Memristor-Based Coupled Neural Networks via ω-Measure

Synchronization of Delayed Memristor-Based Neural Networks via Pinning Control With Local Information

In this article, a novel pinning control method, only requiring information from partial nodes, is developed to synchronize drive-response memristor-based neural networks (MNNs) with time delay. An improved mathematical model of MNNs is established to describe the dynamic behaviors of MNNs accurately. In the existing literature, pinning controllers for synchronization of drive-response systems were designed based on information of all nodes, but in some specific situations, the control gains may be very large and challenging to realize in practice. To overcome this problem, a novel pinning control policy is developed to achieve synchronization of delayed MNNs, which depends only on local information of MNNs, for reducing communication and calculation burdens. Furthermore, sufficient conditions for synchronization of delayed MNNs are provided. Finally, numerical simulation and comparative experiments are conducted to verify the effectiveness and superiority of the proposed pinning control method.

Exponential synchronization of quaternion-valued memristor-based Cohen-Grossberg neural networks with time-varying delays: norm method

In this paper, the exponential synchronization of quaternion-valued memristor-based Cohen-Grossberg neural networks with time-varying delays is discussed. By using the differential inclusion theory and the set-valued map theory, the discontinuous quaternion-valued memristor-based Cohen-Grossberg neural networks are transformed into an uncertain system with interval parameters. A novel controller is designed to achieve the control goal. With some inequality techniques, several criteria of exponential synchronization for quaternion-valued memristor-based Cohen-Grossberg neural networks are given. Different from the existing results using decomposition techniques, a direct analytical approach is used to study the synchronization problem by introducing an improved one-norm method. Moreover, the activation function is less restricted and the Lyapunov analysis process is simpler. Finally, a numerical simulation is given to prove the validity of the main results.

Matrix Measure-Based Event-Triggered Impulsive Quasi-Synchronization on Coupled Neural Networks

In this article, the quasi-synchronization for a kind of coupled neural networks with time-varying delays is investigated via a novel event-triggered impulsive control approach. In view of the randomly occurring uncertainties (ROUs) in the communication channels, the global quasi-synchronization for the coupled neural networks within a given error bound is considered instead of discussing the complete synchronization. A kind of distributed event-triggered impulsive controllers is presented with considering the Bernoulli stochastic variables based on ROUs, which works at each event-triggered impulsive instant. According to the matrix measure method and the Lyapunov stability theorem, several sufficient conditions for the realization of the quasi-synchronization are successfully derived. Combining with the mathematical methodology with the formula of variation of parameters and the comparison principle for the impulsive systems with time-varying delays, the convergence rate and the synchronization error bound are precisely estimated. Meanwhile, the Zeno behaviors could be eliminated in the coupled neural network with the proposed event-triggered function. Finally, a numerical example is presented to prove the results of theoretical analysis.

Fixed-time synchronization for quaternion-valued memristor-based neural networks with mixed delays

In this paper, the fixed-time synchronization (FXTSYN) of unilateral coefficients quaternion-valued memristor-based neural networks (UCQVMNNs) with mixed delays is investigated. A direct analytical approach is suggested to obtain FXTSYN of UCQVMNNs utilizing one-norm smoothness in place of decomposition. When dealing with drive-response system discontinuity issues, use the set-valued map and the differential inclusion theorem. To accomplish the control objective, innovative nonlinear controllers and the Lyapunov functions are designed. Furthermore, some criteria of FXTSYN for UCQVMNNs are given using inequality techniques and the novel FXTSYN theory. And the accurate settling time is obtained explicitly. Finally, in order to show that the obtained theoretical results are accurate, useful, and applicable, numerical simulations are presented at the conclusion.

Event-triggered control for robust exponential synchronization of inertial memristive neural networks under parameter disturbance

Synchronization of memristive neural networks (MNNs) by using network control scheme has been widely and deeply studied. However, these researches are usually restricted to traditional continuous-time control methods for synchronization of the first-order MNNs. In this paper, we study the robust exponential synchronization of inertial memristive neural networks (IMNNs) with time-varying delays and parameter disturbance via event-triggered control (ETC) scheme. First, the delayed IMNNs with parameter disturbance are changed into first-order MNNs with parameter disturbance by constructing proper variable substitutions. Next, a kind of state feedback controller is designed to the response IMNN with parameter disturbance. Based on feedback controller, some ETC methods are provided to largely decrease the update times of controller. Then, some sufficient conditions are provided to realize robust exponential synchronization of delayed IMNNs with parameter disturbance via ETC scheme. Moreover, the Zeno behavior will not happen in all ETC conditions shown in this paper. Finally, numerical simulations are given to verify the advantages of the obtained results such as anti-interference performance and good reliability.

Strictly intermittent quantized control for fixed/predefined-time cluster lag synchronization of stochastic multi-weighted complex networks

This article addresses the fixed-time (F-T) and predefined-time (P-T) cluster lag synchronization of stochastic multi-weighted complex networks (SMWCNs) via strictly intermittent quantized control (SIQC). Firstly, by exploiting mathematical induction and reduction to absurdity, a novel F-T stability lemma is proved and an accurate estimation of settling time (ST) is obtained. Subsequently, by virtue of the proposed F-T stability, some simple conditions that ensure the F-T cluster lag synchronization of SMWCNs are derived by developing a SIQC strategy. Furthermore, the P-T cluster lag synchronization is also explored based on a SIQC design, where the ST can be predefined by an adjustable constant of the controller. Note that the designed controllers here are simpler and more economical than the traditional design whose the linear part is still activated during the rest interval. Finally, two numerical examples are provided to verify the effectiveness of the theoretical results.

Fixed/Predefined-time synchronization of memristor-based complex-valued BAM neural networks for image protection

This paper investigates the fixed-time synchronization and the predefined-time synchronization of memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs) with leakage time-varying delay. First, the proposed neural networks are regarded as two dynamic real-valued systems. By designing a suitable feedback controller, combined with the Lyapunov method and inequality technology, a more accurate upper bound of stability time estimation is given. Then, a predefined-time stability theorem is proposed, which can easily establish a direct relationship between tuning gain and system stability time. Any predefined time can be set as controller parameters to ensure that the synchronization error converges within the predefined time. Finally, the developed chaotic MCVBAMNNs and predefined-time synchronization technology are applied to image encryption and decryption. The correctness of the theory and the security of the cryptographic system are verified by numerical simulation.

Multimode function multistability for Cohen-Grossberg neural networks with mixed time delays

In this paper, we are concerned with the multimode function multistability for Cohen-Grossberg neural networks (CGNNs) with mixed time delays. It is introduced the multimode function multistability as well as its specific mathematical expression, which is a generalization of multiple exponential stability, multiple polynomial stability, multiple logarithmic stability, and asymptotic stability. Also, according to the neural network (NN) model and the maximum and minimum values of activation functions, n pairs of upper and lower boundary functions are obtained. Via the locations of the zeros of the n pairs of upper and lower boundary functions, the state space is divided into ∏_i=1ⁿ(2H_i+1) parts correspondingly. By virtue of the reduction to absurdity, continuity of function, Brouwer's fixed point theorem and Lyapunov stability theorem, the criteria for multimode function multistability are acquired. Multiple types of multistability, including multiple exponential stability, multiple polynomial stability, multiple logarithmic stability, and multiple asymptotic stability, can be achieved by selecting different types of function P(t). Two numerical examples are offered to substantiate the generality of the obtained criteria over the existing results.

Observer-Based Quasi-Synchronization of Delayed Dynamical Networks With Parameter Mismatch Under Impulsive Effect

This article focuses on the observer-based quasi-synchronization problem of delayed dynamical networks with parameter mismatch under impulsive effect. First, since the state of each node is unknown in the real situation, the state estimation strategy is proposed to estimate the state of each node, so as to design an appropriate synchronization controller. Then, the corresponding controller is constructed to synchronize the slave nodes with their leader node. In this article, we take the impulsive effect into consideration, which means that an impulsive signal will be applied to the system every so often. Due to the existence of parameter mismatch and time-varying delay, by constructing an appropriate Lyapunouv function, we will eventually obtain a differential equation with constant and time-varying delay terms. Then, we analyze its trajectory by introducing the Cauchy matrix and prove its boundedness by contradiction. Finally, a numerical simulation is presented to illustrate the validness of obtained results.

Qualitative Analysis and Bifurcation in a Neuron System With Memristor Characteristics and Time Delay

This article focuses on the hybrid effects of memristor characteristics, time delay, and biochemical parameters on neural networks. First, we propose a novel neuron system with memristor and time delays in which the memristor is characterized by a smooth continuous cubic function. Second, the existence of equilibria of this type of neuron system is examined in the parameter space. Sufficient conditions that ensure the stability of equilibria and occurrence of pitchfork bifurcation are given for the memristor-based neuron system without delay. Third, some novel criteria of the addressed neuron system are constructed for guaranteeing the delay-dependent and delay-independent stability. The specific conditions are provided for Hopf bifurcations, and the properties of Hopf bifurcation are ascertained using the center manifold reduction and the normal form theory. Moreover, there exists a phenomenon of bistability for the delayed memristor-based neuron system having three equilibria. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

Global Exponential Synchronization of Coupled Delayed Memristive Neural Networks With Reaction-Diffusion Terms via Distributed Pinning Controls

This article presents new theoretical results on global exponential synchronization of nonlinear coupled delayed memristive neural networks with reaction-diffusion terms and Dirichlet boundary conditions. First, a state-dependent memristive neural network model is introduced in terms of coupled partial differential equations. Next, two control schemes are introduced: distributed state feedback pinning control and distributed impulsive pinning control. A salient feature of these two pinning control schemes is that only partial information on the neighbors of pinned nodes is needed. By utilizing the Lyapunov stability theorem and Divergence theorem, sufficient criteria are derived to ascertain the global exponential synchronization of coupled neural networks via the two pining control schemes. Finally, two illustrative examples are elaborated to substantiate the theoretical results and demonstrate the advantages and disadvantages of the two control schemes.

Recent Advances on Dynamical Behaviors of Coupled Neural Networks With and Without Reaction-Diffusion Terms

Recently, the dynamical behaviors of coupled neural networks (CNNs) with and without reaction-diffusion terms have been widely researched due to their successful applications in different fields. This article introduces some important and interesting results on this topic. First, synchronization, passivity, and stability analysis results for various CNNs with and without reaction-diffusion terms are summarized, including the results for impulsive, time-varying, time-invariant, uncertain, fuzzy, and stochastic network models. In addition, some control methods, such as sampled-data control, pinning control, impulsive control, state feedback control, and adaptive control, have been used to realize the desired dynamical behaviors in CNNs with and without reaction-diffusion terms. In this article, these methods are summarized. Finally, some challenging and interesting problems deserving of further investigation are discussed.

New Criteria on Global Stabilization of Delayed Memristive Neural Networks With Inertial Item

In this paper, we are concerned with global stabilization for a kind of delayed memristive neural network with an inertial term. By building a new Lyapunov functional and designing a feedback controller, we obtain some new results on global stabilization of the addressed delayed memristive inertial neural networks (MINNs). An adaptive control strategy is also designed to realize the global stabilization. Compared with the reduced-order method used in the existing literature, we consider the stabilization directly from the MINNs themselves without a reduced-order method. In addition, the new results proposed here are shown as algebraic criteria, which are easy to test. At last, some simulations are given to show the validity of the derived criteria.

Improved Sliding Mode Control for Finite-Time Synchronization of Nonidentical Delayed Recurrent Neural Networks

This brief further explores the problem of finite-time synchronization of delayed recurrent neural networks with the mismatched parameters and neuron activation functions. An improved sliding mode control approach is presented for addressing the finite-time synchronization problem. First, by employing the drive-response concept and the synchronization error of drive-response systems, a novel integral sliding mode surface is constructed such that the synchronization error can converge to zero in finite time along the constructed integral sliding mode surface. Second, a suitable sliding mode controller is designed by relying on Lyapunov stability theory such that all system state trajectories can be driven onto the predefined sliding mode surface in finite time. Moreover, it is found that the presented control approach can be conveniently verified and does not need to solve any linear matrix inequality (LMI) to guarantee the finite-time synchronization of delayed recurrent neural networks. Finally, three numerical examples are exploited to demonstrate the effectiveness of the presented control approach.

Finite-Time Passivity of Adaptive Coupled Neural Networks With Undirected and Directed Topologies

In this paper, the finite-time passivity (FTP) problem for two classes of coupled neural networks (CNNs) with adaptive coupling weights is discussed. By selecting appropriate adaptive laws and controllers, several FTP conditions are given for CNNs with undirected and directed topologies. Furthermore, some finite-time synchronization conditions are also established by employing the FTP of the CNNs. At last, two numeral examples are used to check the correctness of the obtained criteria.

Global Stabilization of Fractional-Order Memristor-Based Neural Networks With Time Delay

This paper addresses the global stabilization of fractional-order memristor-based neural networks (FMNNs) with time delay. The voltage threshold type memristor model is considered, and the FMNNs are represented by fractional-order differential equations with discontinuous right-hand sides. Then, the problem is addressed based on fractional-order differential inclusions and set-valued maps, together with the aid of Lyapunov functions and the comparison principle. Two types of control laws (delayed state feedback control and coupling state feedback control) are designed. Accordingly, two types of stabilization criteria [algebraic form and linear matrix inequality (LMI) form] are established. There are two groups of adjustable parameters included in the delayed state feedback control, which can be selected flexibly to achieve the desired global asymptotic stabilization or global Mittag-Leffler stabilization. Since the existing LMI-based stability analysis techniques for fractional-order systems are not applicable to delayed fractional-order nonlinear systems, a fractional-order differential inequality is established to overcome this difficulty. Based on the coupling state feedback control, some LMI stabilization criteria are developed for the first time with the help of the newly established fractional-order differential inequality. The obtained LMI results provide new insights into the research of delayed fractional-order nonlinear systems. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed theoretical results.

Finite-time and fixed-time anti-synchronization of Markovian neural networks with stochastic disturbances via switching control

This paper proposes a unified theoretical framework to study the problem of finite/fixed-time drive-response anti-synchronization for a class of Markovian stochastic neural networks. State feedback switching controllers without the sign function are designed to achieve the finite/fixed-time anti-synchronization of the addressed systems. Compared with the existing synchronization criteria, our results indicate that the controllers via the switching control without the sign function are given with less conservativeness, and the controllers without any sign function can deal with the chattering problem. By employing Lyapunov functional method and properties of the Weiner process, several finite/fixed-time synchronization criteria are presented and the corresponding settling times are calculated as well. Finally, three numerical examples are provided to illustrate the effectiveness of the theoretical results.

Effects of Subsystem and Coupling on Synchronization of Multiple Neural Networks With Delays via Impulsive Coupling

This paper from new perspectives discusses the global synchronization of multiple recurrent neural networks (MNNs) with time delays via impulsive coupling. A new concept (coupling strength) is introduced, it is a variable parameter and plays a key role on synchronization. The selection of coupling strength can bring more convenience to the design of the impulsive coupling controller. Four results are presented for the synchronization of MNNs with time delays by using impulsive coupling with the coupling gain and variable topology, where two results are dependent on topology and other two results are independent on topological connectivity. In our results, the effects of each NN, coupling topology, and coupling strength can be positive or negative role on synchronization. In addition, three examples are presented to test our results in the theory analysis.

Hybrid Control Scheme for Projective Lag Synchronization of Riemann–Liouville Sense Fractional Order Memristive BAM NeuralNetworks with Mixed Delays

This sequel is concerned with the analysis of projective lag synchronization of Riemann–Liouville sense fractional order memristive BAM neural networks (FOMBNNs) with mixed time delays via hybrid controller. Firstly, a new type of hybrid control scheme, which is the combination of open loop control and adaptive state feedback control is designed to guarantee the global projective lag synchronization of the addressed FOMBNNs model. Secondly, by using a Lyapunov–Krasovskii functional and Barbalet’s lemma, a new brand of sufficient criterion is proposed to ensure the projective lag synchronization of the FOMBNNs model considered. Moreover, as special cases by using a hybrid control scheme, some sufficient conditions are derived to ensure the global projective synchronization, global complete synchronization and global anti-synchronization for the FOMBNNs model considered. Finally, numerical simulations are provided to check the accuracy and validity of our obtained synchronization results.

Stability of Singular Discrete-Time Neural Networks With State-Dependent Coefficients and Run-to-Run Control Strategies

In this brief, sustaining and intermittent run-to-run controllers are designed to achieve the stability of singular discrete-time neural networks with state-dependent coefficients. The controllers are designed for two reasons: 1) it is very difficult and almost impossible to only measure the in situ feedback information for the controllers and 2) the controllers may not always exist at any time. The stability is then established for singular discrete-time neural networks with state-dependent coefficients. Finally, numerical simulations are shown to illustrate the usefulness of the obtained criteria.

Exponential Synchronization of Networked Chaotic Delayed Neural Network by a Hybrid Event Trigger Scheme

This paper is concerned with the exponential synchronization for master-slave chaotic delayed neural network with event trigger control scheme. The model is established on a network control framework, where both external disturbance and network-induced delay are taken into consideration. The desired aim is to synchronize the master and slave systems with limited communication capacity and network bandwidth. In order to save the network resource, we adopt a hybrid event trigger approach, which not only reduces the data package sending out, but also gets rid of the Zeno phenomenon. By using an appropriate Lyapunov functional, a sufficient criterion for the stability is proposed for the error system with extended ( , , )-dissipativity performance index. Moreover, hybrid event trigger scheme and controller are codesigned for network-based delayed neural network to guarantee the exponential synchronization between the master and slave systems. The effectiveness and potential of the proposed results are demonstrated through a numerical example.

Synchronization Analysis of Inertial Memristive Neural Networks with Time-Varying Delays

This paper investigates the global exponential synchronization and quasi-synchronization of inertial memristive neural networks with time-varying delays. By using a variable transmission, the original second-order system can be transformed into first-order differential system. Then, two types of drive-response systems of inertial memristive neural networks are studied, one is the system with parameter mismatch, the other is the system with matched parameters. By constructing Lyapunov functional and designing feedback controllers, several sufficient conditions are derived respectively for the synchronization of these two types of drive-response systems. Finally, corresponding simulation results are given to show the effectiveness of the proposed method derived in this paper.

Finite-Time Stabilization of Delayed Memristive Neural Networks: Discontinuous State-Feedback and Adaptive Control Approach

In this paper, a general class of delayed memristive neural networks (DMNNs) system described by functional differential equation with discontinuous right-hand side is considered. Under the extended Filippov-framework, we investigate the finite-time stabilization problem for DMNNs by using the famous finite-time stability theorem and the generalized Lyapunov functional method. To do so, we design two classes of novel controllers including discontinuous state-feedback controller and discontinuous adaptive controller. Without assuming the boundedness and monotonicity of the activation functions, several sufficient conditions are given to stabilize the states of this class of DMNNs in finite time. Moreover, the upper bounds of the settling time for stabilization are estimated. Finally, numerical examples are provided to demonstrate the effectiveness of the developed method and the theoretical results.