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This paper is devoted to investigating discrete-time fractional-order delayed quaternion-valued neural networks (DFDQNNs) by utilizing direct quaternion approach. Firstly, a novel lemma and its two corresponding corollaries have been proposed for estimating nabla fractional difference of the quaternion-valued Lyapunov function. Then, the existence and uniqueness of equilibrium point for DFDQNNs is proved by constructing a new quaternion-valued contraction mapping. In addition, by means of our designed Lyapunov functions and the effective feedback controller as well as neoteric nabla difference inequalities, some sufficient criteria have been obtained to ensure the global Mittag–Leffler stability and Mittag–Leffler synchronization of DFDQNNs, respectively. Finally, some numerical examples are provided to verify the yielded results. [ABSTRACT FROM AUTHOR]

It is well known that weighted sum of node states plays an essential role in function implementation of neural networks. Therefore, this paper proposes a new weighted sum synchronization model for memristive neural networks. Unlike the existing synchronization models of memristive neural networks which control each network node to reach synchronization, the proposed model treats the networks as dynamic entireties by weighted sum of node states and makes the entireties instead of each node reach expected synchronization. In this paper, weighted sum complete synchronization and quasi-synchronization are both investigated by designing feedback controller and aperiodically intermittent controller, respectively. Meanwhile, a flexible control scheme is designed for the proposed model by utilizing some switching parameters and can improve anti-interference ability of control system. By applying Lyapunov method and some differential inequalities, some effective criteria are derived to ensure the synchronizations of memristive neural networks. Moreover, the error level of the quasi-synchronization is given. Finally, numerical simulation examples are used to certify the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

In this paper, we have made an effort to investigate the general decay projective synchronization (GDPS) problem of a type of delayed memristor-based BAM neural networks. First, we introduced a type of novel nonlinear controller. Then, we derived some sufficient conditions ensuring the GDPS of considered networks by employing differential inclusion theory and using well-known Lyapunov functional method. Lastly, an example is given to show the correctness of obtained results. To the authors' knowledge, the results derived in this paper are the only available ones on the projective synchronization of BAM neural networks, combining the three main factors, i.e., memristor, general decay and time-varying delays. [ABSTRACT FROM AUTHOR]

In this paper, Harris' Hawks weight optimization-guided artificial neural learning-based quicker session key coordination for Industrial Internet-of-Things (IIoT) to enhance the security of Critical Energy Infrastructure (CEI) is proposed. Transportation, telecommunications, healthcare, finance, and defense are all being revolutionized by the energy industry's digitization. CEI is widely dispersed, resulting in complex cyber-physical networks that require constant monitoring and quick recovery to avoid cyberattacks. Substantial efforts were made in this regard to tackle the key exchange problem in IIoT devices, the majority of which have depended on traditional approaches. Existing solutions fail to adequately resolve the security and privacy issues that IIoT systems face. This study proposes a Triple Layer Vector-Valued Neural Network (TLVVNN) to cope with the problem. However, research into optimizing the value of neural weights for quicker neural synchronization is rare. In this case, Harris' Hawks is used to optimizing the neural network's weight vector for quicker coordination. The coordinated weight becomes the session key once this process is accomplished. This technique has several advantages, including (1) Generation of session key via mutual neural synchronization over the public channel. (2) It enables Harris' Hawks-based neural weight vector optimization for faster neural synchronization across public channels. (3) Vector inputs and weights are taken into consideration for TLVVNN networks. (4) The internal structure of the TLVVNN is complex by three hidden layers. As a result, the attacker might have a lot of difficulties determining the internal architecture. (5) Several pairs of variable-length session keys are generated by TLVVNN. (6) It prevents impersonation, geometric, brute force, and majority assaults. Tests to validate the performance of the proposed methodology are carried out, and the results show that the proposed methodology outperforms similar approaches already in use. [ABSTRACT FROM AUTHOR]

This paper focuses on stability and synchronization of fractional-order Hopfield neural networks. By taking information on activation functions into account, two novel convex Lyapunov functions are constructed: one is a fractional-order-dependent Lyapunov function, and the other is a new quadratic Lyapunov function. Based on these two Lyapunov functions, together with a fractional-order differential inequality, a fractional-order-dependent Mittag–Leffler stability criterion is derived for fractional-order Hopfield neural networks, which is in the form of linear matrix inequalities (LMIs). Moreover, a Mittag–Leffler synchronization criterion in terms of LMIs is presented for drive-response fractional-order Hopfield neural networks under linear control. Finally, three numerical examples are provided to indicate the benefits and less conservatism of the obtained criteria in this paper. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the issue of the finite-time adaptive synchronization and finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays. For synchronizing the drive-response memristive neural networks in finite time, an adaptive state-feedback controller and a state-feedback controller are proposed, respectively. Then by using the theories of differential inclusions and set-valued map, the synchronization issue of drive-response memristive neural networks with discontinuous activation functions and mixed time-varying delays is transformed into the stabilization issue of the error system. Moreover, based on the stability theory, Forti Lemma and Hardy inequality, some novel algebraic synchronization criteria are deduced to ensure the finite-time adaptive synchronization and finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays under the adaptive state-feedback controller and the state-feedback controller. And the settling times for finite-time adaptive synchronization and finite-time synchronization are given. Furthermore, it is hard to estimate the initial conditions for a large system, so the settling times in this paper are not dependent on initial conditions of system. Finally, an example is provided to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we are concerned with the finite-time synchronization for a class of complex-valued neural networks with time delays. Instead of using some finite-time stability theorems which are recently widely applied to investigating the finite-time synchronization for neural networks, by means of using integral inequality method, two novel sufficient conditions on the finite-time synchronization for the above delayed complex-valued neural networks are established. Our results and method on finite-time synchronization for the above neural networks are new and complementary to the existing papers. [ABSTRACT FROM AUTHOR]

This paper is concerned with the synchronization of bi-directional associative memory (BAM) neural networks with diffusion and time-varying delays, in which both synchronizing and desynchronizing impulses are considered. Due to the existence of the diffusion effect in artificial neural networks, synchronization control involves the dynamical behaviors of master–slave systems both in space and time. An impulsive pinning controller is designed for realizing the spatio-temporal synchronization of neural networks. By the Lyapunov functional theory and the comparison principle, exponential synchronization criteria are established, which consist of algebraic inequalities and are easy to implement. Two numerical examples show that controlling only a portion of neurons in the slave neural network can achieve the synchronization of master–slave systems. [ABSTRACT FROM AUTHOR]

This paper studies the passivity and synchronization problems of delayed coupled memristive reaction–diffusion neural networks (CMRDNNs) by utilizing two pinning control schemes, respectively. Firstly, a nodes-based controller is added to the delayed coupled memristive reaction–diffusion neural network model, and some sufficient conditions are derived to ensure the passivity and synchronization of the presented network through constructing appropriate Lyapunov functionals. Additionally, with the help of an edges-based pinning adaptive strategy and inequality techniques, several passivity criteria are further established. Moreover, a similar pinning control method is employed in order to guarantee the synchronization of delayed CMRDNNs. Eventually, two examples are provided to confirm the validity of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the leader-following synchronization of time-delay neural networks with impulsive control involving delayed impulse. A comparison principle for systems with delayed impulses is proposed, where the effect of time delay in impulses is fully considered. Applying impulsive control theory, some sufficient conditions for synchronization of coupled time-delay neural networks via delayed impulses are derived analytically. An example is given to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper focuses on the global exponential synchronization problem for a class of inertial reaction-diffusion coupled neural networks with proportional delay. Through a variable transformation, the inertial reaction-diffusion neural networks are transformed into neural networks with first-order time and space derivative of the states. By taking new Lyapunov-Krasovskii functional, utilizing Wirtinger inequality, a sufficient criterion is obtained to make the addressed networks globally exponentially synchronized onto an isolated node via periodically intermittent feedback controllers. The width index, convergence rate and control gain are given through rigorous mathematical proof. Wirtinger inequality is employed to deal with the reaction-diffusion terms in a symmetric matrix form. The obtained results are easy to be verified by linear matrix inequality toolbox. The results here are also applicable to feedback control for general reaction-diffusion neural networks and inertial neural networks without any other conditions. Finally, the effectiveness and merits of the devised controllers are validated by two simulation experiments. [ABSTRACT FROM AUTHOR]

This paper investigates the global asymptotical synchronization of two nonidentical complex-valued neural networks (CVNNs) with leakage delay and time-varying delays via integral sliding mode control approach. A suitable sliding surface and an appropriate Lyapunov–Krasovskii functional are constructed. By using free-weighting matrix method combined with inequality technique, a sliding mode controller is designed to ensure the synchronization for the considered CVNNs. The obtained criterion is presented in the form of complex-valued linear matrix inequalities (LMIs), which could be calculated through YALMIP with solver of SDPT3 in MATLAB. An example is provided to demonstrate the obtained theoretical result. [ABSTRACT FROM AUTHOR]

This paper concerns globally exponential synchronization for a class of impulsive networks with time-delays. The strategy is based on pinning control: single controller is designed to pin the whole network and realize synchronization. Some new conditions are imposed on impulsive sequences, which make the results obtained in this paper less conservative. A numerical example is supplied to illustrate the validity of the main results. [ABSTRACT FROM AUTHOR]

This paper investigates the periodicity and synchronization of inertial memristive neural networks with supremums and time delays. The analysis in this paper employs the results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. Further, by employing the second order differential inclusion theory and then choosing suitable variable transformation, the original system can be transformed into first order differential equations. By using the matrix measure method and Halany inequality techniques, the sufficient condition that guarantee the global exponential synchronization of drive-response system of coupled inertial memristive neural networks via the state feedback controller is derived. Furthermore, the global exponential periodicity of the addressed neural networks is also discussed. Finally, numerical examples and simulations are given to demonstrate the validation of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive synchronization for time-delay neutral-type multi-slave neural networks with Markovian jumping parameters and stochastic noise is researched. The adaptive synchronization model which contains a drive system and multiple response systems is presented. By using of the generalized It o ^ ’ s formula and the M-matrix method, the sufficient condition is obtained to guarantee that the error control system is stable, and the update law of the feedback controller is designed to ensure that every slave system synchronizes with master system. Finally, a numerical example is given to illustrate the effectiveness of the method and result obtained in this paper. [ABSTRACT FROM AUTHOR]

This study is focused on the issue of adaptive exponential synchronization for a general class of memristive neural networks (MNNs) with mixed time-varying delays. A new and simple adaptive controller with feedback control law is designed to achieve exponential synchronization by using Lyapunov functional method. The adaptive controller proposed in the paper possesses a powerful adaptive capability that it can be utilized for various MNNs with different mathematical definitions of memristor. In addition, no excessive calculations such as solving linear matrix inequality or computing algebraic conditions are required in our synchronization criteria. We also present two synchronization conditions for a special class of MNNs that part or even all of the system׳s right-hand is reduced to be continuous when activation functions are zero at the neuron׳s switching points. And two lemmas are introduced to modify a misunderstanding in this situation in some previous papers. Finally, an example with numerical simulations is presented to illustrate the efficiency and accuracy of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of stochastic Cohen–Grossberg neural networks driven by G -Brownian motion (G -SCGNNs, in short). We establish the exponential synchronization of G -SCGNNs by applying inequality technique, k th vertex- G -Lyapunov functions, graph-theory and state feedback control technique. A concrete example is given to verify the obtained theory. [ABSTRACT FROM AUTHOR]

• As the first attempt, the operation of each subsystem in the S-MJNNs at different-time-scales is fully considered. • The developed extended dissipativity performance index is more general. • The parameters uncertainties of the S-MJNNs under consideration randomly occur, which is more realistic. This paper concentrates on the synchronization problem for singularly perturbed neural networks with semi-Markov jump parameters and randomly occurring uncertainties. A continuous-time semi-Markov process is utilized to model the stochastic switching of the parameters. An independent singularly perturbed parameter is separated through the use of singularly perturbed slow-fast decomposition method. Some sufficient conditions are deduced to ensure that the error system is synchronized and meets the extended dissipative property. In particular, the uncertainty of the networks is considered to occur randomly, which is more realistic than the existing work. Moreover, the efficiency of the presented method is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new fixed-time stability theorem. Numerical simulations show that our upper bound estimate for the settling time is much smaller than those in the existing fixed-time stability theorems. Based on the new fixed-time stability theorem, we investigate the fixed-time synchronization of memristive neural networks (MNNs) by adopting a delay-dependent feedback controller. Numerical simulations are provided to demonstrate the correctness of our theoretical results and the superiority of the new fixed-time stability theorem. [ABSTRACT FROM AUTHOR]

The problem of local synchronization control for chaotic neural networks with sampled-data and saturating actuators is investigated in this paper. The intervals from the sampling instant t k to its next instant t k + 1 are assumed to be within a sampling interval. By taking advantage of characteristic information on the whole sampling interval, a new two-sided sampling-interval-dependent discontinuous Lyapunov functional is first constructed, which depends on the available information of both the intervals from t k to t and from t to t k + 1. Then, by utilizing the Lyapunov functional, a novel sampling-interval-dependent stability condition is derived, rendering the synchronization error systems stable. Moreover, an optimization approach is provided to design desired sampled-data controllers such that the set of admissible initial conditions can be maximized. Finally, the effectiveness and benefits of the presented method is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

State estimation and synchronization of neural networks (NNs) have recently received ever-increasing research interests due to a large number of successful applications in various fields such as repetitive learning, classification of patterns, nonlinear control, adaptive control, image processing, and so forth. Owing to limited communication bandwidth, the network-induced phenomena and the adopted communication scheduling may cause inevitable negative effects or the degradation of dynamical performance of NNs. This paper, from the perspective of dynamical behavior, renders a comprehensive summary on the recent advances of communication-embedded NNs and their application in nonlinear control. First, some common network-induced phenomena and communication protocols are roughly introduced from both models and mechanisms. Then, the state estimation and synchronization analysis of various NNs with network-induced phenomena are systematically reviewed and some interesting results are separately presented. Furthermore, the latest advances for the cases with communication protocols are profoundly surveyed from three aspects: state estimation, synchronization analysis and applications in control realm. Finally, some challenged problems are listed and several potential future research directions are highlighted. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a coupled reaction–diffusion neural networks (CRDNNs) model with multiple time-delays and uncertain inner coupling matrices is presented, and then some sufficient conditions are derived to make sure such network is passive. Subsequently, the uncertain CRDNNs with multiple time-delays and state couplings are considered, and the passivity criteria are given by exploiting some inequality techniques and Lyapunov functional. Similarly, the synchronization for such two networks are also investigated. Eventually, we provided two numerical examples to verify the validity of these acquired results. [ABSTRACT FROM AUTHOR]

Abstract Stability and synchronization for Riemann-Liouville fractional-order time-delayed inertial neural networks are investigated in this paper. The model of fractional-order inertial neural network is proposed, which is more general and less conservative than the integer-order inertial neural network. Two lemmas on the composition properties of Riemann-Liouville fractional-order derivative and integral are given. Based on the composition properties of Riemann-Liouville fractional-order derivative, the original inertial system is transferred into conventional system through the proper variable substitution. Serval novel and effective feedback controllers are proposed for different cases of fractional-order time-delayed inertial neural networks, such that synchronization between the salve system and the master system can be achieved. In addition, stability conditions for a class of fractional-order time-delayed inertial neural networks are derived. Furthermore, three numerical examples are provided to show the validity and feasibility of the approaches. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the problem on the exponential synchronization of inertial neural networks with discrete and finite distributed time-varying delays using intermittent control. Two kinds of time varying delays are considered: one is whose derivatives are strictly smaller than one and the other is without any restriction on the delay derivatives. Based on Lyapunov–Krasovskii functional method and applying inequality techniques, some new delay-dependent criteria are obtained to ensure the global exponential synchronization for the discussed networks, which are very simple to implement in practice and reduce the computational burden. Moreover, the exponential synchronization convergence rates depend on the norm, the transformation parameters, the control parameters and the width index of the control. Finally, some numerical examples are presented to demonstrate the validity of our results. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the problem of pinning synchronization for memristive neural networks with time-varying delays via aperiodic intermittent control. By applying aperiodic intermittent control to partial nodes of the memristive neural networks, some new general criteria for global exponential synchronization are derived based on the theory of nonsmooth analysis. The obtained results indicate that it is the control rates rather than the control periods or control widths are involved in the synchronization criteria. In addition, a feasible region of the control gains and control rates is established for achieving global exponential synchronization. Finally, numerical simulations are given to verify the correctness of our theoretical analysis. [ABSTRACT FROM AUTHOR]

Abstract This paper focus on the synchronization of complex-valued neural networks (CVNNs) with both discrete and distributed two additive time-varying delays. By applying matrix inequality technique and exploiting reciprocally convex approach, several delay-dependent criteria are presented in the form of linear matrix inequalities (LMIs) to ensure the global synchronization of CVNNs via structuring an appropriate Lyapunov–Krasovskii functional. An example with simulations is provided to ensure the feasibility of the obtained result. [ABSTRACT FROM AUTHOR]

Abstract Proportional delay, which is different from time-varying delays and distributed delay, is a kind of unbounded delay. The proportional delay system as an important mathematical model often rises in some various fields such as control theory, physics and biology systems. This paper is concerned with the finite-time and the fixed-time synchronization problem for a class of inertial neural networks with multi-proportional delays. First, by constructing a proper variable substitution, the original inertial neural networks with multi-proportional delays can be rewritten as a first-order differential system. Second, by constructing Lyapunov functionals and by using analytical techniques, and together with novel control algorithms, some new and effective criteria are established to achieve finite-time and fixed-time synchronization of the master/slave of addressed systems. Finally, several examples and their simulations are given to illustrate the effectiveness of the proposed method. Furthermore, a secure communication synchronization problem is presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract This paper addresses the synchronization problem for neutral-type neural networks with Lévy noise and sampled-data loss. An event-triggered control scheme is employed to overcome occasional sampled-data loss and solve the synchronization problem, which is a sampling controller with selection mechanism. Under the scheme, the sampled data is not transmitted to plant unless a predetermined threshold condition is violated. The Lyapunov method and linear matrix inequality technique are employed to analyze almost sure stability of synchronization error system. Finally, the numerical example shows the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

Abstract The feed-forward neural network is an artificial neural network, which is used extensively in deep learning models, wherein synaptic weight and characteristic time play very important role in information moves. In this paper, based on a feed-forward multilayer (ten layers) Hindmarsh–Rose (HR) neural network, the effects of synaptic weight and characteristic time on the signal propagation are investigated under the cases of continuous and transient external stimulated current, respectively. In the presence of continuous external stimulated current triggering the discharge of neurons, it is found that a random input signal driven by Gaussian white noise can be transmitted from input layer to next layers, and the propagation of weak spike train is gradually disappeared in the following layers when the synaptic weight is small. However, by choosing the appropriate values of synaptic weight and characteristic time, the mean firing rate of neurons in output layer is increased and the synchronization of neural firing in the following layers can be triggered. In the presence of transient (a short period) stimulated current triggering the discharge of neurons on the input layer, the firing rate of neurons cannot be transmitted from the input layer to the following layers with a small synaptic weight. Moreover, with the increasing of the synaptic weight, the mean firing rates of neurons in the following layers are higher than that in input layer, and the neurons in the following layers can be excited. [ABSTRACT FROM AUTHOR]

Abstract In this paper, synchronization-based passivity of coupled neural networks (CNNs) with partial and event-triggered communication is discussed. Event conditions are designed based on the partial couplings among neural networks. A regrouping method is introduced to build a channel Laplacian matrix which contains the structural information of both couplings and channels. Based on such new matrix, a novel error system is established for the purpose of synchronizing the CNNs. A sufficient condition for solving the synchronization problem of partially coupled neural networks is given. Moreover, the same condition can also verify the passivity of networks when noise is nonzero. Finally, a numerical example demonstrates the effectiveness of the control mechanism. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the passivity and synchronization of multiple delayed coupled reaction–diffusion neural networks (MDCRDNNs) with different dimensions of output and input vectors by means of impulsive control. By introducing suitable Lyapunov functionals and employing some analytical techniques, sufficient conditionsare derived to guarantee the passivity and globally exponential synchronization of MDCRDNNs under impulsive control. Finally, three simulation examples are performed to illustrate the results. [ABSTRACT FROM AUTHOR]

Abstract This paper is devoted to fixed-time synchronization for coupled Cohen–Grossberg neural networks (CGNNs) with constant coupling and delayed coupling. By constructing suitable Lyapunov functional, a criterion is obtained to guarantee that coupled CGNNs achieves fixed-time synchronization. Furthermore, when parameter uncertainties occur, a sufficient condition for ensuring robust fixed-time synchronization of coupled CGNNs is presented. Similarly, the case that coupled CGNNs including delayed coupling is also discussed. Finally, two numerical examples are provided to show the availability for the acquired results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we investigate the finite-time boundedness ( FTB ) and finite-time stabilization ( FTS ) of uncertain switched delayed neural networks of neutral type. Some sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to guarantee the FTB and FTS of the uncertain delayed switched neural networks of neutral type by using the multiple Lyapunov–Krasovskii functional, free-weighting matrix method, and average dwell time (ADT) methods, which are dependent on both the transmission delay and time delay in neutral term. Moreover, a state feedback controller is designed via the established LMIs. Finally, two examples are given to illustrate the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with fixed-time synchronization of coupled delayed neural networks with discontinuous or continuous activation functions. Two discontinuous control protocols under undirected or directed topologies are proposed to guarantee that coupled delayed neural networks achieve synchronization with a desired trajectory in fixed time, respectively. Several sufficient criteria for fixed-time synchronization are obtained. Furthermore, an upper bound of the settling time is theoretically estimated, which is independent on initial conditions. Finally, two numerical examples are given to illustrate the effectiveness of the synchronization criteria. [ABSTRACT FROM AUTHOR]

Abstract In this paper, based on the asymptotic expansion of Mittag-Leffler function and the fractional comparison principle, an improved fractional Halanay inequality with time-varying coefficients is proved by introducing parameters λ i and δ. The fractional autonomous Halanay inequality is generalized to the fractional non-autonomous case. Moreover, based on the improved fractional Halanay inequality and Lyapunov functional method, a novel sufficient condition on self synchronization of the fractional non-autonomous Hopfield neural networks with time delay is obtained. Finally, three numerical examples are given to demonstrate the effectiveness of proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with two coupled memristive delayed neural networks with different dimensions of input and output. The essential difference between them is whether coupling delay is incorporated in the network model. First, we respectively analyze the passivity of the presented network models, and some passivity conditions are deduced under the help of some inequality techniques. Then, considering that the networks cannot achieve passivity by themselves in some cases, an edge-based adaptive strategy is developed for guaranteeing the passivity, input-strict passivity and output-strict passivity of the raised networks. At the end, the correctness of the acquired criteria is verified by two illustrative examples. [ABSTRACT FROM AUTHOR]

This paper investigates the sampled-data synchronization of switched neural networks with time-varying discrete and distributed delays. Considering that the system switching may happen during a sampling interval, the asynchronous phenomenon is taken into account for the sampled-data control process. By utilizing multiple Lyapunov functions and average dwell time property, sufficient conditions are derived to guarantee the exponential stability of the error between the master and slave neural networks. Based on this, sampled-data controller is further designed so that the master and the slave systems are synchronized with a prescribed performance index. Finally, a numerical example is provided to illustrate the validness and effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, exponential synchronization of coupled inertial neural networks (CINNs) with bounded time-varying discrete delay and infinite-time distributed delay (mixed delays) is considered by designing quantized pinning controllers. By designing novel Lyapunov–Krasovskii functionals and using new weighted integral inequalities, delay-dependent criteria formulated by linear matrix inequality (LMI) are obtained. Different from existing ones, the designed Lyapunov–Krasovskii functionals include negative terms, which lead to less conservative results. Numerical simulations verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of finite-time adaptive synchronization is investigated for two different delayed neural networks with unknown parameters. Two adaptive control approaches are designed in order to synchronize the neural networks in finite time. The first controller fully involves the information of time-varying delay and the second one is delay-independent under the case that time-varying delay is unknown. By utilizing the Lyapunov stability theory, sufficient conditions are proposed to guarantee the finite-time synchronization of the addressed neural networks. In addition, the settling time for synchronization is estimated. Finally, two numerical simulations are used to illustrate the correctness and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The problem of synchronization via sampled-data and saturating controller is considered for stochastic time-delay neural networks with Lévy noise and Markovian switching parameters in this paper. By using of the generalized Itô׳s formula and the Lyapunov functional method, an LMI-based sufficient condition is established to ensure the mean square synchronization of the master system and the slave system. Meanwhile, the gain of the sample data and saturating controller is determined. The sufficient condition depends on not only the switching mode and time-delay, but also the upper and the lower bound of sampling intervals. A numerical example is provided to verify the usefulness of the criterion proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates a new hybrid projective synchronization scheme between two coupled fractional-order complex networks with different sizes. The hybrid projective synchronization studied in this paper includes complete synchronization of the states of the nodes in each network and projective synchronization of the states of a pair of nodes from both networks. Based on the stability theorem of fractional-order differential system and adaptive control technique, some sufficient conditions for guaranteeing the existence of the hybrid projective synchronization are derived. Two examples are given to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The cooperative exponential synchronization of multi-agent chaotic delayed neural networks (DNNs) with switching topology, stochastic disturbance and impulsive disturbance is investigated in this paper. Based on the Lyapunov stability theory, algebraic graph theory, matrix theory and the helpful stochastic Halanay inequality technique, some sufficient conditions are presented to guarantee the cooperative exponential synchronization for multi-agent chaotic DNNs with switching topology. Compared with the existing works about synchronization (or consensus) of multi-agent systems, the proposed method in this paper can provide a more general framework for the cooperative synchronization of nonlinear multi-agent systems with or without time delays, stochastic and impulsive disturbances. The famous master–slave (drive-response) synchronization of chaotic DNNs is a special case of this paper, and therefore the derived results can also be favorable for practical application in secure communication. Simulation results finally verify the effectiveness of the proposed synchronization control algorithm. [ABSTRACT FROM AUTHOR]

This paper is concerned with the issue of pinning synchronization of a general model of complex dynamical networks, which can well describe practical architectures of many realistic complex systems. Compared with some existing works, the distinctive feature of the considered model in this paper includes (i) the network topologies with variable structures corresponding directed graph; (ii) the multi-linked configuration with nonlinear coupling and time-varying delays. Some generic criteria for pinning global synchronization of such dynamical network are presented based on Lyapunov stability theory on delayed dynamical systems. It is shown that these criteria can provide a novel and effective adaptive pinning strategy, which is very convenient to implement in practice since the design of the adaptive control law is independent of time-varying delays. Furthermore, it is interesting to find that when the nodes with low in-degrees are pinned firstly, the pinning control scheme is more efficient. Subsequently, the theoretic results are applied to a general two-linked network consisting of Hopfield neuron oscillator. Finally, numerical simulations demonstrate that the proposed pinning adaptive synchronization criteria are practical and effective to pin two-linked Hopfield neural networks to an equilibrium, periodic orbit and chaotic attractor. [ABSTRACT FROM AUTHOR]

This paper is concerned with finite-time synchronization for a class of delayed neural networks with Cohen-Grossberg type. Different from the existing related results, the time-delayed feedback strategy is utilized to investigate finite-time synchronization of delayed Cohen-Grossberg neural networks. By constructing Lyapunov functions and using differential inequalities, several new and effective criteria are derived to realize local and global synchronization in finite time of the addressed neural networks based on two different time-delayed feedback controllers. Besides, the upper bounds of the settling time of synchronization are estimated. Furthermore, as corollaries, some sufficient conditions are given to achieve finite-time synchronization of delayed cellular neural networks. Finally, some numerical examples are provided to verify the theoretical results established in this paper. [ABSTRACT FROM AUTHOR]

Finite-time synchronization means the optimality in convergence time, thus many contributions have been made to it in the literature. However, to the best of our knowledge, most of the existing results on finite-time synchronization do not include time-delay. Considering the fact that time-delays especially infinite-time distributed delays are inevitably existing in neural networks, this paper aims to study global synchronization in finite time of neural networks with both time-varying discrete delay and infinite-time distributed delay (mixed delays). The techniques that we apply in this paper are not only different from the techniques employed in existing papers, but also applicable to differential systems with or without delay. Based on new Lyapunov-Krasovskii functional candidate and the new analysis techniques, sufficient conditions guaranteeing the finite-time synchronization of the addressed neural networks are derived by using a class of simple discontinuous state feedback controller. Conditions for realizing finite-time synchronization of neural networks with finite-time distributed delay and without delay are also given. Moreover, estimation of the upper bound of synchronization-time is also provided for neural networks with finite-time distributed delay and without delay. It is shown that the synchronization-time depends on both the initial values and the time-delays of the drive-response systems. Numerical examples demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a finite-time lag synchronization of coupled neural networks with time delay is investigated. By means of the Lyapunov stability theory, a feedback controller is designed for achieving lag synchronization between two delayed neural networks systems in finite time. Paper extends some basic results from the area of finite time to time-delay systems. Numerical simulations on coupled Lu neural systems illustrate the effectiveness of the results. [Copyright &y& Elsevier]

This paper aims to study the finite-time synchronization (i.e., synchronization in finite-time sense) of Cohen–Grossberg neural networks with mixed time delays (both time-varying discrete delay and infinite-time distributed delay). By constructing Lyapunov–Krasovskii functional candidates and using inequality techniques, some new sufficient conditions are derived to design the discontinuous state feedback controllers such that the addressed neural networks can be synchronized in a finite settling time, where the upper bounds of the settling time of synchronization are estimated. The effects of unknown or known time-delay are seriously taken into account, respectively, which lead to two different delay-independent discontinuous state feedback controllers. Thus our results can be applied to the finite-time synchronization of neural networks whether the time delay can be measured or not. As some special cases, our results also improve some recent works. Simulation results show the applicability and the advantages of the proposed finite-time controllers. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the anti-synchronization of master–slave neural networks with time delays. By dividing the whole anti-synchronization process into two procedures: the absolute value of error state e i ( t ) flowing from the initial state to 1, then from 1 to 0, i = 1 , … , n , it gets a new viewpoint and a clear illustration on how controller works to the systems. And combining the H o ¨ lder inequality and other techniques, rigorous analysis gives that, each component of error state e ( t ) ( t  ≥ 0) would flow to 1 in finite time, and continue to flow to 0 in fixed time. A numerical example is presented to illustrate the efficiency and effectiveness of our obtained results. [ABSTRACT FROM AUTHOR]

This paper deals with the passivity and synchronization problems for two types of coupled reaction–diffusion Cohen–Grossberg neural networks (CRDCGNNs). On the one side, a CRDCGNNs model with state coupling is introduced, and several sufficient conditions which ensure the passivity and synchronization of this type of network are deduced respectively by resorting to some inequality techniques and Lyapunov functional method. On the other side, considering that the different diffusion of each node may give rise to different changes of other nodes in reaction–diffusion networks, we also carry out some investigations on the passivity and synchronization of CRDCGNNs with spatial diffusion coupling. Finally, the correctness of the obtained research results are corroborated by two illustrative examples. [ABSTRACT FROM AUTHOR]

This paper investigates the general decay synchronization (GDS) of a type of neural networks (NNs) with general neuron activation functions and varying-time delays. By introducing suitable Lyapunov functional and employing useful inequality techniques, some simple and useful sufficient conditions ensuring the GDS of considered NNs are established via designing a novel nonlinear feedback controller. In addition, two examples are presented to show the effectiveness of the established theoretical results. The polynomial synchronization, asymptotical synchronization, and exponential synchronization can be seen the special cases of the GDS. [ABSTRACT FROM AUTHOR]