Impulsive Effects on Quasi-Synchronization of Neural Networks With Parameter Mismatches and Time-Varying Delay

Synchronization of time-delay dynamical networks via hybrid delayed impulses

This paper investigates the synchronization problem of time-delay dynamical networks by means of hybrid delayed impulses, where synchronizing impulses and desynchronizing impulses can occur simultaneously. Some sufficient synchronization conditions are established based on Razumikhin-type inequality and Lyapunov function. These conditions do not place any limitation on the magnitude of time-delay in dynamical networks. To be specific, it can be less than or greater than the length of impulses intervals and has no magnitude relationship with delays in impulses. Moreover, results indicate that delays in impulses have positive contributions to synchronization. The effectiveness of the theoretical results is demonstrated by two numerical examples.

DoS attacks resilience of heterogeneous complex networks via dynamic event-triggered impulsive scheme for secure quasi-synchronization

This paper addresses the secure quasi-synchronization issue of heterogeneous complex networks (HCNs) under aperiodic denial-of-service (DoS) attacks with dynamic event-triggered impulsive scheme (ETIS). The heterogeneity of networks and the aperiodic DoS attacks, which hinder communication channels and synchronization goals, present challenges to the analysis of secure quasi-synchronization. The ETIS leverages impulsive control and dynamic event-triggered scheme (ETS) to handle the network heterogeneity and the DoS attacks. We give specific bounds on the attack duration and frequency that the network can endure, and obtain synchronization criteria that relate to event parameters, attack duration, attack frequency, and impulsive gain by the variation of parameter formula and recursive methods. Moreover, we prove that the dynamic ETS significantly reduces the controller updates, saves energy without sacrificing the system decay rate, and prevents the Zeno phenomenon. Finally, we validate our control scheme with a numerical example.

Novel criteria of sampled-data synchronization controller design for gated recurrent unit neural networks under mismatched parameters

Synchronization between neural networks (NNs) has been intensively investigated to analyze stability, convergence properties, neuronal behaviors and response to various inputs. However, synchronization techniques of NNs with gated recurrent units (GRUs) have not been provided until now due to their complicated nonlinearity. In this paper, we address the sampled-data synchronization problems of GRUs for the first time, and propose controller design methods using discretely sampled control inputs to synchronize master and slave GRUs. The master and slave GRUs are mathematically modeled as a linear parameter varying (LPV) system in which the parameter of the slave GRUs is constructed independently of the master GRUs. This distinctive modeling feature provides flexibility to extend the existing master and slave NNs into a more general structure. Indeed, the sampled-data synchronization can be achieved by formulating the design condition in terms of linear matrix inequalities (LMIs). The novel sampled-data synchronization criteria are devised by combining the H∞ controller design with the looped-functional approach. The synthesized synchronization controllers guarantee not only asymptotic stability of the synchronization error system with aperiodic sampling, but also provides a satisfactory H∞ control performance. Moreover, the communication efficiency is improved by using the proposed method in which the sampled-data synchronization controller is combined with the event-triggered mechanism. Finally, the numerical example validates the proposed theoretical contributions via simulation results.

Matrix measure-based distributed impulsive consensus on nonlinear multi-agent systems with mixed time-varying delays

This paper concentrates on researching the global and exponential leader-following consensus issue for an array of nonlinear multi-agent systems with the system time-varying delay and the distributed time-varying delay. An innovative distributed impulsive controller is proposed to force the states of all agents to track the trajectories of leader agent. By jointly introducing the matrix measure protocol, the comparison principle for impulsive systems, and the average impulsive interval, sufficient criteria for the realization of leader-following consensus are derived. In addition, considering different functions of impulsive signal, two different convergence rates are precisely estimated by utilizing the parameter variation formula, respectively. Finally, two numerical examples are given to demonstrate the effectiveness of proposed control strategy and the rightness of theoretical analysis.

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.

Interval Bipartite Synchronization of Multiple Neural Networks in Signed Graphs

Interval bipartite consensus of multiagents described by signed graphs has received extensive concern recently, and the rooted cycles play a critical role in stabilization, while the structurally balanced graphs are essential to achieve bipartite consensus. However, the gauge transformation used in the linear system is no longer feasible in the nonlinear case. This article addresses interval bipartite synchronization of multiple neural networks (NNs) in a signed graph via a Lyapunov-based approach, extending the existing work to a more practical but complicated case. A general matrix M in signed graphs is introduced to construct the novel Lyapunov functions, and sufficient conditions are obtained. We find that the rooted cycles and the structurally balanced graphs are essential to stabilize and achieve bipartite synchronization. More importantly, we discover that the nonrooted cycles are crucial in reaching interval bipartite synchronization, not previously mentioned. Several examples are presented to illustrate interval bipartite synchronization of multiple NNs with signed graphs.

Quasi-synchronization of drive-response systems with parameter mismatch via event-triggered impulsive control

In this paper, an event-triggered impulsive control method is proposed to investigate the quasi-synchronization of drive-response systems with parameter mismatch, which integrates the event-triggered control and impulsive control together. The impulsive instants are event-triggered and determined by a certain state-dependent triggering law. Sufficient conditions for achieving quasi-synchronization are achieved. The synchronization error is shown to be no more than a nonzero bound. Furthermore, Zeno-behavior of impulsive instants is excluded. Finally, a numerical example is presented to verify the validity of the theoretical results.

Multiple Mismatched Synchronization for Coupled Memristive Neural Networks With Topology-Based Probability Impulsive Mechanism on Time Scales

This article is concerned with the exponential synchronization of coupled memristive neural networks (CMNNs) with multiple mismatched parameters and topology-based probability impulsive mechanism (TPIM) on time scales. To begin with, a novel model is designed by taking into account three types of mismatched parameters, including: 1) mismatched dimensions; 2) mismatched connection weights; and 3) mismatched time-varying delays. Then, the method of auxiliary-state variables is adopted to deal with the novel model, which implies that the presented novel model can not only use any isolated system (regard as a node) in the coupled system to synchronize the states of CMNNs but also can use an external node, that is, not affiliated to the coupled system to synchronize the states of CMNNs. Moreover, the TPIM is first proposed to efficiently schedule information transmission over the network, possibly subject to a series of nonideal factors. The novel control protocol is more robust against these nonideal factors than the traditional impulsive control mechanism. By means of the Lyapunov-Krasovskii functional, robust analysis approach, and some inequality processing techniques, exponential synchronization conditions unifying the continuous-time and discrete-time systems are derived on the framework of time scales. Finally, a numerical example is provided to illustrate the effectiveness of the main results.

Dynamic Self-Triggered Impulsive Synchronization of Complex Networks With Mismatched Parameters and Distributed Delay

Synchronization of complex networks with nonlinear couplings and distributed time-varying delays is investigated in this article. Since the mismatched parameters of individual systems, a kind of leader-following quasisynchronization issues is analyzed via impulsive control. To acquire appropriate impulsive intervals, the dynamic self-triggered impulsive controller is devoted to predicting the available instants of impulsive inputs. The proposed controller ensures the control effects while reducing the control costs. In addition, the updating laws of the dynamic parameter is settled in consideration of error bounds to adapt to the quasisynchronization. With the utilization of the Lyapunov stability theorem, comparison method, and the definition of average impulsive interval, sufficient conditions for realizing the synchronization within a specific bound are derived. Moreover, with the definition of average impulsive gain, the parameter variation scheme is extended from the fixed impulsive effects case to the time-varying impulsive effects case. Finally, three numerical examples are given to show the effectiveness and the superiority of proposed mathematical deduction.

Matrix Measure-Based Projective Synchronization on Coupled Neural Networks With Clustering Trees

This article mainly studies the projective quasisynchronization for an array of nonlinear heterogeneous-coupled neural networks with mixed time-varying delays and a cluster-tree topology structure. For the sake of the mismatched parameters and the mutual influence among distinct clusters, the exponential and global quasisynchronization within a prescribed error bound instead of complete synchronization for the coupled neural networks with clustering trees is investigated. A kind of pinning impulsive controllers is designed, which will be imposed on the selected neural networks with some largest norms of error states at each impulsive instant in different clusters. By employing the concept of the average impulsive interval, the matrix measure method, and the Lyapunov stability theorem, sufficient conditions for the realization of the cluster projective quasisynchronization are derived. Meanwhile, in terms of the formula of variation of parameters and the comparison principle for the impulsive systems with mixed time-varying delays, the convergence rate and the synchronization error bound are precisely estimated. Furthermore, the synchronization error bound is efficiently optimized based on different functions of the impulsive effects. Finally, a numerical experiment is given to prove the results of theoretical analysis.

Impulsive strategies in nonlinear dynamical systems: A brief overview

The studies of impulsive dynamical systems have been thoroughly explored, and extensive publications have been made available. This study is mainly in the framework of continuous-time systems and aims to give an exhaustive review of several main kinds of impulsive strategies with different structures. Particularly, (i) two kinds of impulse-delay structures are discussed respectively according to the different parts where the time delay exists, and some potential effects of time delay in stability analysis are emphasized. (ii) The event-based impulsive control strategies are systematically introduced in the light of several novel event-triggered mechanisms determining the impulsive time sequences. (iii) The hybrid effects of impulses are emphatically stressed for nonlinear dynamical systems, and the constraint relationships between different impulses are revealed. (iv) The recent applications of impulses in the synchronization problem of dynamical networks are investigated. Based on the above several points, we make a detailed introduction for impulsive dynamical systems, and some significant stability results have been presented. Finally, several challenges are suggested for future works.

Cluster Synchronization of Coupled Neural Networks With Lévy Noise via Event-Triggered Pinning Control

Cluster synchronization means that all multiagents are divided into different clusters according to the equations or roles of nodes in a complex network, and by designing an appropriate algorithm, each cluster can achieve synchronization to a certain value or an isolated node. However, the synchronization values between different clusters are different. With a feedback controller based on the calculation of the control input value and a trigger condition leading to the updating instants, this article introduces the trigger mechanism and designs a new data sampling strategy to achieve cluster synchronization of the coupled neural networks (CNNs), which reduces the number of updates of the controller, thereby reducing unnecessary waste of limited resources. In addition, an example proposes a synchronization algorithm and gives iterative procedures to calculate the trigger instants and prove the validity of the theoretical results.

Exponential Stability of Fractional-Order Switched Systems With Mode-Dependent Impulses and Its Application

Most exiting results for impulsive switched systems (ISSs) are mainly built on the synchronous switching and impulses case; however, the impulses can not only occur in switched interval including switched instants but also the switched signals may exist between two impulsive points in practical instants. Under asynchronous impulses and switching signals, the main objective of this article is to study the exponential stability of fractional-order hybrid systems. In order to better characterize stability, some novel criteria are presented by adopting the mode-dependent average impulsive interval and induction method. The obtained impulsive switched criteria lead to a tradeoff between fractional-order α and impulsive strength. Especially, the impulsive effects (positive or negative) with the order α are also discussed in detail, which extends the previous integer order results. Moreover, numerical examples are given to interpret and verify the effectiveness of the obtained criteria.

Quasisynchronization of Memristive Neural Networks With Communication Delays via Event-Triggered Impulsive Control

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

Quasisynchronization of Heterogeneous Neural Networks With Time-Varying Delays via Event-Triggered Impulsive Controls

Time delays are unavoidable since they are ubiquitous and may have a great impact on the performance of neural networks. Resources efficiency is a common concern in many networked systems with limited resources. This article investigates quasisynchronization of the heterogeneous neural networks with time-varying delays via event-triggered impulsive controls which combine the impulsive control and the event-triggered technique. The centralized and distributed event-triggered impulsive controls are, respectively, presented. The suitable Lyapunov functions are constructed, and the triggering functions are derived, which guarantee that not only are the synchronization errors less than a non-negative bound but also the Zeno behaviors can be eliminated. It is suggested that the distributed one has great superiority in taking up fewer resources compared with the time-triggered impulsive control. Numerical examples are proposed to verify the validity of the centralized and distributed control methods.

Quasisynchronization of Heterogeneous Dynamical Networks via Event-Triggered Impulsive Controls

The time-triggered impulsive control of complex homogeneous dynamical networks has received wide attention due to its occasional occupation of the communication channels. This article is devoted to quasisynchronization of heterogeneous dynamical networks via event-triggered impulsive controls with less channel occupation. Two kinds of triggered mechanisms, that is, the centralized event-triggered mechanism in which the control is updated based upon the state information of all nodes, and the distributed event-triggered mechanism where the control is updated according to the state information of each node and its neighboring node, are proposed, respectively, such that the synchronization error between the heterogeneous dynamical networks and a virtual target is not more than a nonzero bound. What is more, the Zeno behavior is shown to be excluded. It is found that the combination method of the event-triggered control and the impulsive control, that is, the distributed event-triggered impulsive control has the advantage of low-energy consumption and takes up many fewer communication channels over the time-triggered impulsive control. Two numerical examples are conducted to illustrate the effectiveness of the proposed event-triggered impulsive controls.

Guaranteed Cost Finite-Time Control of Uncertain Coupled Neural Networks

This article investigates a robust guaranteed cost finite-time control for coupled neural networks with parametric uncertainties. The parameter uncertainties are assumed to be time-varying norm bounded, which appears on the system state and input matrices. The robust guaranteed cost control laws presented in this article include both continuous feedback controllers and intermittent feedback controllers, which were rarely found in the literature. The proposed guaranteed cost finite-time control is designed in terms of a set of linear-matrix inequalities (LMIs) to steer the coupled neural networks to achieve finite-time synchronization with an upper bound of a guaranteed cost function. Furthermore, open-loop optimization problems are formulated to minimize the upper bound of the quadratic cost function and convergence time, it can obtain the optimal guaranteed cost periodically intermittent and continuous feedback control parameters. Finally, the proposed guaranteed cost periodically intermittent and continuous feedback control schemes are verified by simulations.

Fixed/Preassigned-time synchronization of quaternion-valued neural networks via pure power-law control

The fixed-time synchronization and preassigned-time synchronization of quaternion-valued neural networks are concerned in this article. By developing fixed-time stability and proposing a pure power-law control scheme, some simple conditions are obtained to realize fixed-time synchronization of quaternion-valued neural networks and the upper bound of the synchronized time is provided. Furthermore, the preassigned-time synchronization of quaternion-valued neural networks is investigated based on pure power-law control design, where the synchronization time is preassigned in advance and the control gains are finite. Note that the designed controllers in this paper are the pure power-law forms, which are simpler and more effective compared with the traditional design composed of the linear part and power-law part. Eventually, an example is given to illustrate the feasibility and validity of the results obtained.

Event-Based Synchronization for Multiple Neural Networks With Time Delay and Switching Disconnected Topology

This article discusses the synchronization problem for a class of multiple delayed neural networks (MDNNs) with a directed switching topology by using an event-triggering strategy. First, a new differential inequality with delay is shown, which is a generalization of Halanay-type inequalities. Then, the sufficient conditions of event-based synchronization (quasisynchronization) for MDNN with sequentially connected topology are obtained by using this inequality and the iterative method. Meantime, we prove that Zeno behavior can be avoided under the designed event-triggering rules. As an extension, MDNN with jointly connected topology is also discussed. Finally, a numerical example is listed to illustrate the results in theory analysis.

New effective approach to quasi synchronization of coupled heterogeneous complex networks

This short paper addresses quasi synchronization of linearly coupled heterogeneous systems. Similarity and difference between the complete synchronization of linearly coupled homogeneous systems and the quasi synchronization of linearly coupled heterogeneous systems will be revealed.

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.

Fixed-Time Synchronization of Coupled Neural Networks With Discontinuous Activation and Mismatched Parameters

This article is concerned with fixed-time synchronization of the nonlinearly coupled neural networks with discontinuous activation and mismatched parameters. First, a novel lemma is proposed to study fixed-time stability, which is less conservative than those in most existing results. Then, based on the new lemma, a discontinuous neural network with mismatched parameters will synchronize to the target state within a settling time via two kinds of unified and simple controllers. The settling time is theoretically estimated, which is independent of the initial values of the considered network. In particular, the estimated settling time is closer to the real synchronization time than those given in the existing literature. Finally, two numerical simulations are presented to illustrate the effectiveness and correctness of our results.

Exponential Stability of Discrete-Time Neural Networks With Large Delay

We study the exponential stability of discrete-time neural networks (NNs) with a time-varying delay which contains a few intermittent large delays (LDs). By modeling the considered discrete-time NN as a discrete-time switched NN which contains two subsystems and one of them may be unstable over the LD periods (LDPs), switching techniques are employed to analyze the problem. Delay-dependent exponential stability conditions to check the frequency and the length of the LDs allowed for guaranteeing the exponential stability are proposed by applying a novel Lyapunov-Krasovskii functional (LKF) with LDP-based terms, Wirtinger-based summation inequality, and reciprocally convex combination technique. Based on these conditions, associated evaluation algorithms are developed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

Quasisynchronization of Discrete-Time Inertial Neural Networks With Parameter Mismatches and Delays

Contrary to many existing works based on the continuous-time inertial neural network, this article considers the quasisynchronization issue for the discrete-time inertial neural network. To obtain the main results, we adopt the generalized matrix-measure concept. A condition ensuring the quasisynchronization is attained at first. To make the result less conservative, further analysis based on the generalized matrix measure is proceeded. An example is given to demonstrate the validity and effectiveness of the main results.

Synchronization of Nonidentical Neural Networks With Unknown Parameters and Diffusion Effects via Robust Adaptive Control Techniques

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

Observer-Based Impulsive Synchronization for Neural Networks With Uncertain Exchanging Information

This article investigates synchronization for a group of discrete-time neural networks (NNs) with the uncertain exchanging information, which is caused by the uncertain connection weights among the NNs nodes, and they are transformed into a norm-bounded uncertain Laplacian matrix. Distributed impulsive observers, which possess the advantage of reducing the communication load among NNs nodes, are designed to observe the NNs state. The impulsive controller is proposed to improve the efficiency of the controller. An impulsive augmented error system (IAES) is obtained based on the matrix Kronecker product. A sufficient condition is established to ensure synchronization of the group of NNs by proving the stability of the IAES. An iterative algorithm is given to obtain a suboptimal allowed interval of the impulsive signal, and the corresponding gains of the observer and the controller are derived. The developed result is illustrated by a numerical example.

Quasi-Synchronization and Bifurcation Results on Fractional-Order Quaternion-Valued Neural Networks

In this article, the quasi-synchronization and Hopf bifurcation issues are investigated for the fractional-order quaternion-valued neural networks (QVNNs) with time delay in the presence of parameter mismatches. On the basis of noncommutativity property of quaternion multiplication results, the quaternion network has been split as four real-valued networks. A synchronization theorem for fractional-order QVNNs is derived by employing suitable Lyapunov functional candidate; furthermore, the bifurcation behavior of the hub-structured fractional-order QVNNs with time delay has been investigated. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Impulsive Control of Nonlinear Systems With Time-Varying Delay and Applications

Impulsive control of nonlinear delay systems is studied in this paper, where the time delays addressed may be the constant delay, bounded time-varying delay, or unbounded time-varying delay. Based on the impulsive control theory and some analysis techniques, a new theoretical result for global exponential stability is derived from the impulsive control point of view. The significance of the presented result is that the stability can be achieved via the impulsive control at certain impulse points despite the existence of impulsive perturbations which causes negative effect to the control. That is, the impulsive control provides a super performance to allow the existence of impulsive perturbations. In addition, we apply the theoretical result to the problem of impulsive control of delayed neural networks. Some results for global exponential stability and synchronization control of neural networks with time delays are derived via impulsive control. Three illustrated examples are given to show the effectiveness and distinctiveness of the proposed impulsive control schemes.

Quasi-Synchronization of Discrete-Time Lur'e-Type Switched Systems With Parameter Mismatches and Relaxed PDT Constraints

This paper investigates the problem of quasi-synchronization for a class of discrete-time Lur'e-type switched systems with parameter mismatches and transmission channel noises. Different from the previous studies referring to the persistent dwell-time (PDT) switching signals, the average dwell-time (ADT) constraints combined with the PDT are considered simultaneously in this paper to relax the limitation of dwell-time requirements and to improve the flexibility of the PDT switching signal design. By virtue of the semi-time-varying (STV) Lyapunov function, the synchronization criteria for transmitter-receiver systems in a switched version are obtained to satisfy a prescribed synchronization error bound. An estimate of the synchronization error bound is provided via the reachable set approach and, further, an explicit description of the error bounds is given. Then, sufficient conditions on the existence of STV observers are derived with a predetermined error bound, and the corresponding observer gains are calculated via solving a group of linear matrix inequalities. Finally, the effectiveness and validness of the developed theoretical results are demonstrated via a numerical example.

Projective Synchronization of Delayed Neural Networks With Mismatched Parameters and Impulsive Effects

In this paper, the impulsive effects on projective synchronization between the parameter mismatched neural networks with mixed time-varying delays have been analyzed. Since complete synchronization is not possible due to the existence of parameter mismatch and projective factor, a drive has been taken to achieve the weak projective synchronization of different neural networks under impulsive control strategies. Through the use of matrix measure technique and the extended comparison principle based on the formula of variation of parameters for mixed time-varying delayed impulsive systems, sufficient criteria have been derived for exponential convergence of the networks under the effects of extensive range of impulse. Instead of upper or lower bound of the impulsive interval, the concept of the average impulsive interval is applied to estimate the number of impulsive points in an interval. The concept of calculus is applied for optimizing the synchronization error bounds which are obtained because of different ranges of impulse. Finally, the numerical simulations for various impulsive ranges for different cases are presented graphically to validate the efficiency 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.

Effects of infinite occurrence of hybrid impulses with quasi-synchronization of parameter mismatched neural networks

This article is deeply concerned with the effects of hybrid impulses on quasi-synchronization of neural networks with mixed time-varying delays and parameter mismatches. Hybrid impulses allow synchronizing as well as desynchronizing impulses in one impulsive sequence, so their infinite time occurrence with the system may destroy the synchronization process. Therefore, the effective hybrid impulsive controller has been designed to deal with the difficulties in achieving the quasi-synchronization under the effects of hybrid impulses, which occur all the time, but their density of occurrence gradually decrease. In addition, the new concepts of average impulsive interval and average impulsive gain have been applied to cope with the simultaneous existence of synchronizing and desynchronizing impulses. Based on the Lyapunov method together with the extended comparison principle and the formula of variation of parameters for mixed time-varying delayed impulsive system, the delay-dependent sufficient criteria of quasi-synchronization have been derived for two separate cases, viz., T_a<∞ and T_a=∞. Finally, the efficiency of the theoretical results has been illustrated by providing two numerical examples.