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

Mode-Mixed Effects Based Intralayer-Dependent Impulsive Synchronization for Multiple Mismatched Multilayer Neural Networks

This article focuses on the intralayer-dependent impulsive synchronization of multiple mismatched multilayer neural networks (NNs) with mode-mixed effects. Initially, a novel multilayer NN model that removes the one-to-one interlayer coupling constraint and introduces nonidentical model parameters is first established to meet diverse modeling requirements in complex applications. To help the multilayer target NNs with mismatched connection coefficients and time delays achieve synchronization, the hybrid controller is designed using intralayer-dependent impulsive control and switched feedback control approaches. Furthermore, the mode-mixed effects caused by the intralayer coupling delays and switched intralayer topologies are incorporated into the novel model and analysis method to ensure that the subsystems operating within the current switching interval can effectively use the topology information of the previous switching intervals. Then, a novel analysis framework including super-Laplacian matrix, augmented matrix, and mode-mixed methods is developed to derive the synchronization results. Finally, the main results are verified via the numerical simulation with secure communication.

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.

Adaptive Synchronization of Reaction-Diffusion Neural Networks With Nondifferentiable Delay via State Coupling and Spatial Coupling

In this article, master-slave synchronization of reaction-diffusion neural networks (RDNNs) with nondifferentiable delay is investigated via the adaptive control method. First, centralized and decentralized adaptive controllers with state coupling are designed, respectively, and a new analytical method by discussing the size of adaptive gain is proposed to prove the convergence of the adaptively controlled error system with general delay. Then, spatial coupling with adaptive gains depending on the diffusion information of the state is first proposed to achieve the master-slave synchronization of delayed RDNNs, while this coupling structure was regarded as a negative effect in most of the existing works. Finally, numerical examples are given to show the effectiveness of the proposed adaptive controllers. In comparison with the existing adaptive controllers, the proposed adaptive controllers in this article are still effective even if the network parameters are unknown and the delay is nonsmooth, and thus have a wider range of applications.

Projective Synchronization of Delayed Uncertain Coupled Memristive Neural Networks and Their Application

In this article, the authors analyzed the nonlinear effects of projective synchronization between coupled memristive neural networks (MNNs) and their applications. Since the complete signal transmission is difficult under parameter mismatch and different projective factors, the delays, which are time-varying, and uncertainties have been taken to realize the projective synchronization of MNNs with multi-links under the nonlinear control method. Through the extended comparison principle and a new approach to dealing with the mismatched parameters, sufficient criteria have been determined under different types of projective factors and the framework of the Lyapunov-Krasovskii functional (LKF) for projective convergence of the coupled MNNs. Instead of the classical treatment for secure communication, the concept of error of synchronization between the drive and response systems has been applied to solve the signal encryption/decryption problem. Finally, the simulations in numerical form have been demonstrated graphically to confirm the adaptability of the theoretical results.

Quasi-projective and complete synchronization of discrete-time fractional-order delayed neural networks

This paper presents new theoretical results on quasi-projective synchronization (Q-PS) and complete synchronization (CS) of one kind of discrete-time fractional-order delayed neural networks (DFDNNs). At first, three new fractional difference inequalities for exploring the upper bound of quasi-synchronization error and adaptive synchronization are established by dint of Laplace transform and properties of discrete Mittag-Leffler function, which vastly expand a number of available results. Furthermore, two controllers are designed including nonlinear controller and adaptive controller. And on the basis of Lyapunov method, the aforementioned inequalities and properties of fractional-order difference operators, some sufficient synchronization criteria of DFDNNs are derived. Because of the above controllers, synchronization criteria in this paper are less conservative. At last, numerical examples are carried out to illustrate the usefulness of theoretical upshots.

Master-Slave Synchronization of Neural Networks With Unbounded Delays via Adaptive Method

Master-slave synchronization of two delayed neural networks with adaptive controller has been studied in recent years; however, the existing delays in network models are bounded or unbounded with some derivative constraints. For more general delay without these restrictions, how to design proper adaptive controller and prove rigorously the convergence of error system is still a challenging problem. This article gives a positive answer for this problem. By means of the stability result of unbounded delayed system and some analytical techniques, we prove that the traditional centralized adaptive algorithms can achieve global asymptotical synchronization even if the network delays are unbounded without any derivative constraints. To describe the convergence speed of the synchronization error, adaptive designs depending on a flexible ω -type function are also provided to control the synchronization error, which can lead exponential synchronization, polynomial synchronization, and logarithmically synchronization. Numerical examples on delayed neural networks and chaotic Ikeda-like oscillator are presented to verify the adaptive designs, and we find that in the case of unbounded delay, the intervention of ω -type function can promote the realization of synchronization but may destroy the convergence of control gain, and this however will not happen in the case of bounded delay.

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.

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.

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.

Projective quasi-synchronization of coupled memristive neural networks with uncertainties and impulsive effect

The dynamic behavior of memristive neural networks (MNNs), including synchronization, effectively keeps the robotic stability against numerous uncertainties from the mimic of the human brain. However, it is challenging to perform projective quasi-synchronization of coupled MNNs with low-consumer control devices. This is partly because complete synchronization is difficult to realize under various projective factors and parameter mismatch. This article aims to investigate projective quasi-synchronization from the perspective of the controller. Here, two approaches are considered to find the event-triggered scheme for lag synchronization of coupled MNNs. In the first approach, the projective quasi-synchronization issue is formulated for coupled MNNs for the first time, where the networks are combined with time-varying delays and uncertainties under the constraints imposed by the frequency of controller updates within limited system communication resources. It is shown that our methods can avoid the Zeno-behavior under the newly determined triggered functions. In the second approach, following classical methods, a novel projective quasi-synchronization criterion that combines the nonlinear property of the memristor and the framework of Lyapunov-Krasovskii functional (LKF) is proposed. Simulation results indicate that the proposed two approaches are useful for coupled MNNs, and they have less control cost for different types of quasi-synchronization.

Construction of a Knowledge Map of Speech Emotion Features Based on Impulse-Coupled Neural Networks

This paper constructs knowledge graphs of speech emotion feature to support the expression of rich semantic information due to their unique graphical structure and to provide new ideas for studying speech emotion recognition recommendations. Impulse-coupled neural networks, as a mathematical abstraction of the visual properties of the human eye, have been widely used in various fields of speech processing. In this paper, we take the classical impulse-coupled neural network model as the research object, aiming to explore, analyze, and study the method of constructing knowledge maps of speech emotion features based on the impulse-coupled neural network model, and propose several improved impulse-coupled neural network models, which are used in the fields of target detection, speech segmentation, and quantization compression. This paper further constructs various domain semantic concept maps and performs multidimensional semantic enhancement understanding of search text based on the concept maps and the constructed entity-relationship knowledge maps and proposes a knowledge-based interpretable recommendation method for cloud services and a generalized recommendation and sample enhancement method for cloud scenarios. The fusion algorithm based on multiscale analysis can decompose the source speech into subspeech at different scales and then fuse each subspeech separately, while typical objects in the real world are also composed of many components at different scales. Based on the factors of different degrees in the speech context, the imagery work ruler evaluation model is refined with the basic principles of risk perception and risk resolution in the context, and an exploratory design is carried out separately for the verbal description, graphics, text, color, animation, and sound signals in the audiovisual signal using the workshop format to obtain a large number of design samples and evaluate the important units in turn, finally integrating the context involved in the study. The perceptual design system is given as a specific contextual design method.

Projective Synchronization Analysis of Fractional-Order Neural Networks With Mixed Time Delays

In this article, we analyze the projective synchronization of fractional-order neural networks with mixed time delays. By introducing an extended Halanay inequality that is applicable for the case of fractional differential equations with arbitrary initial time and multiple types of delays, sufficient criteria are deduced for ensuring the projective synchronization of fractional-order neural networks with both discrete time-varying delays and distributed delays. Furthermore, sufficient criteria are presented for ensuring the projective synchronization in the Mittag-Leffler sense if there is no delay in fractional-order neural networks. The results derived herein include complete synchronization, anti-synchronization, and stabilization of fractional-order neural networks as particular cases. Moreover, the testable criteria in this article are a meaningful extension of projective synchronization of neural networks with mixed time delays from integer-order to fractional-order ones. A numerical simulation with four cases is provided to verify the validity of the obtained results.

A New Settling-time Estimation Protocol to Finite-time Synchronization of Impulsive Memristor-Based Neural Networks

In this article, the issues of finite-time synchronization and finite-time adaptive synchronization for the impulsive memristive neural networks (IMNNs) with discontinuous activation functions (DAFs) and hybrid impulsive effects are probed into and elaborated on, where the stabilizing impulses (SIs), inactive impulses (IIs), and destabilizing impulses (DIs) are taken into account, respectively. Not resembling several earlier works, a more extensive range of impulses in the context of impulsive effects has been analyzed without using the known average impulsive interval strategy (AIIS). In light of the theories of differential inclusions and set-valued map, as well as impulsive control, new sufficient criteria with respect to the estimated settling time for synchronization of the related IMNNs are established using two types of switching control approaches, which sufficiently utilize information from not only the SIs, DIs, and DAFs but also the impulse sequences. Two simulation experiments are presented to the efficiency of the proposed results.

Delayed Impulsive Control for Lag Synchronization of Delayed Neural Networks Involving Partial Unmeasurable States

In the framework of impulsive control, this article deals with the lag synchronization problem of neural networks involving partially unmeasurable states, where the time delay in impulses is fully addressed. Since the complexity of external environment and uncertainty of networks, which may lead to a result that the information of partial states is unmeasurable, the key problem for lag synchronization control is how to utilize the information of measurable states to design suitable impulsive control. By using linear matrix inequality (LMI) and transition matrix method coupled with dimension expansion technique, some sufficient conditions are derived to guarantee lag synchronization, where the requirement for information of all states is needless. Moreover, our proposed conditions not only allow the existence of unmeasurable states but also reduce the restrictions on the number of measurable states, which shows the generality of our results and wide-application in practice. Finally, two illustrative examples and their numerical simulations are presented to demonstrate the effectiveness of main 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.

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.