Exponential Synchronization of Coupled Stochastic Memristor-Based Neural Networks With Time-Varying Probabilistic Delay Coupling and Impulsive Delay

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.

Finite-time synchronization for coupled neural networks with time-delay jumping coupling

The finite-time synchronization problem is studied for coupled neural networks (CNNs) with time-delay jumping coupling. Markovian switching topologies, imprecise delay models, uncertain parameters and the unavailable of topology modes are considered in this work. A mode-dependent delay with pre-known conditional probability is built to handle the imprecise delay model problem. A hidden Markov model with uncertain parameters is introduced to describe the mode mismatch problem, and an asynchronous controller is designed. Besides, a set of Bernoulli processes models the random packet dropouts during data communication. Based on Markovian switching topologies, mode-dependent delays, uncertain probabilities and packet dropout, a sufficient condition that guarantees the CNNs reach finite-time synchronization (FTS) is derived. Finally, a numerical example is derived to demonstrate the efficiency of the proposed synchronous technique.

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.

Novel adaptive synchronization in finite-time and fixed-time for impulsive complex networks with semi-Markovian switching

This paper intensively studied the finite-time (FNT) and fixed-time (FXT) synchronization issues for complex networks (CNs) with semi-Markovian switching and impulsive effect. The impulses are assumed to be independent of the semi-Markovian switching. Firstly, a unified FNT and FXT stability criterion of impulsive dynamical system with time-varying delays is extended by comparison principle. Secondly, two novel hybrid control schemes, which are composed of adaptive gain and switching state-feedback are proposed. Thirdly, by employing Kronecker product, Lyapunov-Krasovskii functional and inequality technique, FNT and FXT synchronization criteria for impulsive CNs with semi-Markovian switching are presented in a set of low-dimensional linear matrix inequalities, and the settling times are computed respectively. Finally, simulations are given to verify the proposed adaptive FNT and FXT synchronization criteria.

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.

Globally Adaptive Neural Network Tracking for Uncertain Output-Feedback Systems

This article investigates the problem of global neural network (NN) tracking control for uncertain nonlinear systems in output feedback form under disturbances with unknown bounds. Compared with the existing NN control method, the differences of the proposed scheme are as follows. The designed actual controller consists of an NN controller working in the approximate domain and a robust controller working outside the approximate domain, in addition, a new smooth switching function is designed to achieve the smooth switching between the two controllers, in order to ensure the globally uniformly ultimately bounded of all closed-loop signals. The Lyapunov analysis method is used to strictly prove the global stability under the combined action of unmeasured states and system uncertainties, and the output tracking error is guaranteed to converge to an arbitrarily small neighborhood through a reasonable selection of design parameters. A numerical example and a practical example were put forward to verify the effectiveness of the control strategy.

Improved Results on Fixed-/Preassigned-Time Synchronization for Memristive Complex-Valued Neural Networks

This article concerns the problems of synchronization in a fixed time or prespecified time for memristive complex-valued neural networks (MCVNNs), in which the state variables, activation functions, rates of neuron self-inhibition, neural connection memristive weights, and external inputs are all assumed to be complex-valued. First, the more comprehensive fixed-time stability theorem and more accurate estimations on settling time (ST) are systematically established by using the comparison principle. Second, by introducing different norms of complex numbers instead of decomposing the complex-valued system into real and imaginary parts, we successfully design several simpler discontinuous controllers to acquire much improved fixed-time synchronization (FXTS) results. Third, based on similar mathematical derivations, the preassigned-time synchronization (PATS) conditions are explored by newly developed new control strategies, in which ST can be prespecified and is independent of initial values and any parameters of neural networks and controllers. Finally, numerical simulations are provided to illustrate the effectiveness and superiority of the improved synchronization methodology.

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.

Prefixed-Time Local Intermittent Sampling Synchronization of Stochastic Multicoupling Delay Reaction-Diffusion Dynamic Networks

This article focuses on the problem of prefixed-time synchronization for stochastic multicoupled delay dynamic networks with reaction-diffusion terms and discontinuous activation by means of local intermittent sampling control. Notably, unlike the existing common fixed-time synchronization, this article puts forward a new synchronization concept, prefixed-time synchronization, based on the fact that stochastic noise and discontinuous activation can be seen everywhere in practical engineering, which can effectively perfect and improve the existing works. Specifically, a local intermittent in the time domain and point sampling control strategy in the spatial domain is proposed instead of a simple single intermittent control approach, which greatly reduces the control cost. In addition, by some effective means, including the famous Young's inequality, Jensen's inequality, and Hölder's inequality, we obtain two different synchronization criteria of the networks without delay and with multicoupling delays and deeply reveal the quantitative relationship among control period, point sampling length, and network scale. Finally, a numerical example is given to verify the effectiveness of the developed method and the practicability by Chua's circuit model.

Predefined-Time Stability/Synchronization of Coupled Memristive Neural Networks With Multi-Links and Application in Secure Communication

This paper explores the realization of a predefined-time synchronization problem for coupled memristive neural networks with multi-links (MCMNN) via nonlinear control. Several effective conditions are obtained to achieve the predefined-time synchronization of MCMNN based on the controller and Lyapunov function. Moreover, the settling time can be tunable based on a parameter designed by the controller, which is more flexible than fixed-time synchronization. Then based on the predefined-time stability criterion and the tunable settling time, we propose a secure communication scheme. This scheme can determine security of communication in the aspect of encrypting the plaintext signal with the participation of multi-links topology and coupled form. Meanwhile, the plaintext signals can be recovered well according to the given new predefined-time stability theorem. Finally, numerical simulations are given to verify the effectiveness of the obtained theoretical results and the feasibility of the secure communication scheme.

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.

Adaptive Event-Triggered Synchronization of Reaction-Diffusion Neural Networks

This article focuses on the design of an adaptive event-triggered sampled-data control (ETSDC) mechanism for synchronization of reaction-diffusion neural networks (RDNNs) with random time-varying delays. Different from the existing ETSDC schemes with predetermined constant thresholds, an adaptive ETSDC mechanism is proposed for RDNNs. The adaptive ETSDC mechanism can be promptly adaptively adjusted since the threshold function is based on the current sampled and latest transmitted signals. Thus, the adaptive ETSDC mechanism can effectively save communication resources for RDNNs. By taking the influence of uncertain factors, the random time-varying delays are considered, which belongs to two intervals in a probabilistic way. Then, by constructing an appropriate Lyapunov-Krasovskii functional (LKF), new synchronization criteria are derived for RDNNs. By solving a set of linear matrix inequalities (LMIs), the desired adaptive ETSDC gain is obtained. Finally, the merits of the adaptive ETSDC mechanism and the effectiveness of the proposed results are verified by one numerical example.

Global Exponential Stability of Memristive Neural Networks With Mixed Time-Varying Delays

This article investigates the Lagrange exponential stability and the Lyapunov exponential stability of memristive neural networks with discrete and distributed time-varying delays (DMNNs). By means of inequality techniques, theories of the M-matrix, and the comparison strategy, the Lagrange exponential stability of the underlying DMNNs is considered in the sense of Filippov, and the globally exponentially attractive set is estimated through employing the M-matrix and external input. Especially, when the external input is not concerned, the Lyapunov exponential stability of the corresponding DMNNs is developed immediately in the form of an M-matrix, which contains some published outcomes as special cases. Furthermore, by constructing an M-matrix-based differential system, the Lyapunov exponential stability of the DMNNs is studied, which is less conservative than some existing ones. Finally, three simulation examples are carried out to examine the validness of the theories.

Dynamical and static multisynchronization analysis for coupled multistable memristive neural networks with hybrid control

This paper investigates the dynamical multisynchronization (DMS) and static multisynchronization (SMS) problems for a class of delayed coupled multistable memristive neural networks (DCMMNNs) via a novel hybrid controller which includes delayed impulsive control and state feedback control. Based on the state-space partition method and the geometrical properties of the activation function, each subnetwork has multiple locally exponential stable equilibrium states. By employing a new Halanay-type inequality and the impulsive control theory, some new linear matrix inequalities (LMIs)-based sufficient conditions are proposed. It is shown that the delayed impulsive control with suitable impulsive interval and allowable time-varying delay can still guarantee the DMS and SMS of DCMMNNs. Finally, a numerical example is presented to illustrate the effectiveness of the hybrid controller.

Finite-/Fixed-Time Synchronization of Delayed Coupled Discontinuous Neural Networks With Unified Control Schemes

In this article, it addresses the problem of finite-/fixed-time synchronization of delayed coupled discontinuous neural networks in the unified framework. To achieve the finite-/fixed-time synchronization and precise estimations of setting time, two novel different kinds of controllers are established, in which one is switching. Then, based on the finite-/fixed-time theorem and Lyapunov function theory, some useful criteria are obtained to select suitable controllers' parameters, which can guarantee error systems converge in the finite time/fixed time with respect to coupled neural networks. Moreover, corresponding estimations of the setting time are also provided. Finally, two numerical examples are introduced to show the effectiveness of the proposed control protocols.

Nonseparation Method-Based Finite/Fixed-Time Synchronization of Fully Complex-Valued Discontinuous Neural Networks

This article mainly focuses on the problem of synchronization in finite and fixed time for fully complex-variable delayed neural networks involving discontinuous activations and time-varying delays without dividing the original complex-variable neural networks into two subsystems in the real domain. To avoid the separation method, a complex-valued sign function is proposed and its properties are established. By means of the introduced sign function, two discontinuous control strategies are developed under the quadratic norm and a new norm based on absolute values of real and imaginary parts. By applying nonsmooth analysis and some novel inequality techniques in the complex field, several synchronization criteria and the estimates of the settling time are derived. In particular, under the new norm framework, a unified control strategy is designed and it is revealed that a parameter value in the controller completely decides the networks are synchronized whether in finite time or in fixed time. Finally, some numerical results for an example are provided to support the established theoretical results.

Impulsive Synchronization of Unbounded Delayed Inertial Neural Networks With Actuator Saturation and Sampled-Data Control and its Application to Image Encryption

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

Periodic Event-Triggered Synchronization of Multiple Memristive Neural Networks With Switching Topologies and Parameter Mismatch

This article investigates the synchronization problem of multiple memristive neural networks (MMNNs) in the case of switching communication topologies and parameter mismatch. First, the distributed event-triggered control under continuous sampling conditions is studied. Then, a periodic event-triggered control (PETC) model is proposed to substantially reduce control consumption. Using the Lyapunov method, the properties of M -matrix, and some inequalities, the sufficient criteria of synchronous control are derived. The results can be used in the analysis of other multiagent nonlinear systems. A norm-based threshold function is given to determine the update time of the controller, and it is proved that the trigger condition excludes the Zeno behavior. Subject to parameter mismatch, a quasisynchronous control strategy is proposed, which can be extended to complete synchronization provided that the system mismatch or disturbance disappears. It is worth mentioning that this article introduces the signal function into the controller, so that the theoretical error can be limited to an arbitrarily small range. Furthermore, this new controller is used in the PETC strategy which automatically avoids the Zeno behavior. Finally, one example is given to illustrate our results.

Multi-scroll hidden attractor in memristive HR neuron model under electromagnetic radiation and its applications

This paper aims to propose a novel no-equilibrium Hindmarsh-Rose (HR) neuron model with memristive electromagnetic radiation effect. Compared with other memristor-based HR neuron models, the uniqueness of this memristive HR neuron model is that it can generate multi-scroll hidden attractors with sophisticated topological structures and the parity of the scrolls can be controlled conveniently with changing the internal parameters of the memristor. In particular, the number of scrolls of the multi-scroll hidden attractors is also associated with the intensity of external electromagnetic radiation stimuli. The complex dynamics is numerically studied through phase portraits, bifurcation diagrams, Lyapunov exponents, and a two-parameter diagram. Furthermore, hardware circuit experiments are carried out to demonstrate theoretical analyses and numerical simulations. From the perspective of engineering application, a pseudo-random number generator is designed. Besides, an image encryption application and security analysis are also performed. The obtained results show that the memristive HR neuron model possesses excellent randomness and high security, which is suitable for chaos-based real-world applications.

Extended Robust Exponential Stability of Fuzzy Switched Memristive Inertial Neural Networks With Time-Varying Delays on Mode-Dependent Destabilizing Impulsive Control Protocol

This article investigates the problem of robust exponential stability of fuzzy switched memristive inertial neural networks (FSMINNs) with time-varying delays on mode-dependent destabilizing impulsive control protocol. The memristive model presented here is treated as a switched system rather than employing the theory of differential inclusion and set-value map. To optimize the robust exponentially stable process and reduce the cost of time, hybrid mode-dependent destabilizing impulsive and adaptive feedback controllers are simultaneously applied to stabilize FSMINNs. In the new model, the multiple impulsive effects exist between two switched modes, and the multiple switched effects may also occur between two impulsive instants. Based on switched analysis techniques, the Takagi-Sugeno (T-S) fuzzy method, and the average dwell time, extended robust exponential stability conditions are derived. Finally, simulation is provided to illustrate the effectiveness of the results.

Fixed-time synchronization of stochastic memristor-based neural networks with adaptive control

In this study, we consider the fixed-time synchronization problem for stochastic memristor-based neural networks (MNNs) via two different controllers. First, a new stochastic differential equation is established using differential inclusions and set-valued maps. Next, two kinds of control protocols are designed, including a nonlinear delayed state feedback control scheme and a novel adaptive control strategy, by which fixed-time synchronization of MNNs can be achieved. Then based on stochastic analysis techniques and a Lyapunov function, some sufficient criteria are obtained to ensure that stochastic MNNs achieve stochastic fixed-time synchronization in probability. In addition, the upper bound of the settling time is estimated. Finally, simulation results are provided to demonstrate the validity of the proposed schemes.

Global μ-synchronization of impulsive pantograph neural networks

This paper investigates the problem of global μ-synchronization of impulsive pantograph neural networks. In this paper, new concept of ν-asymptotic periodic impulsive interval T_asy^ν is proposed for pantograph networks. By employing the Lyapunov method combined with the mathematical analysis approach for impulsive systems, some useful criteria are derived to guarantee the global μ-synchronization of coupled pantograph neural networks when the asymptotic logarithmic periodic impulsive interval T_asy^ln<∞ and T_asy^ln=∞, respectively. Especially when T_asy^ln=∞, as long as the networks are unstable, impulsive control cannot achieve synchronization regardless of the size of the impulse gain. Numerical simulations are exploited to illustrate our theoretical results.

Event-Triggered Synchronization Strategy for Multiple Neural Networks With Time Delay

This paper deals with global exponential synchronization of multiple neural networks (NNs) with time delay via a very broad class of event-triggered coupling, in which coupling matrix can be non-Laplacian. Some simple and convenient sufficient conditions are derived to guarantee global exponential synchronization of the coupling NNs under an event-triggered strategy. In particular, the effect of the common subsystem can be positive or negative on the synchronization scheme. Three examples are presented to test the results in theory analysis.

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

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

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.

Non-fragile state estimation for fractional-order delayed memristive BAM neural networks

This paper deals with the non-fragile state estimation problem for a class of fractional-order memristive BAM neural networks (FMBAMNNs) with and without time delays for the first time. By means of a novel transformation and interval matrix approach, non-fragile estimators are designed and parameter mismatch problem is averted. Sufficient criteria are established to ascertain the error system is asymptotically stable based on fractional-order Lyapunov functionals and linear matrix inequalities (LMIs). Two examples are put forward to show the effectiveness of the obtained results.

Synchronization control of quaternion-valued memristive neural networks with and without event-triggered scheme

In this paper, the real-valued memristive neural networks (MNNs) are extended to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established. The problem of master-slave synchronization of this type of networks is investigated in this paper. Two types of controllers are designed: the traditional feedback controller and the event-triggered controller. Corresponding synchronization criteria are then derived based on Lyapunov method. Moreover, it is demonstrated that Zeno behavior can be avoided in case of the event-triggered strategy proposed in this work. Finally, corresponding simulation examples are proposed to demonstrate the correctness of the proposed results derived in this work.

On the validity of memristor modeling in the neural network literature

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks.

Multistability of Delayed Hybrid Impulsive Neural Networks With Application to Associative Memories

The important topic of multistability of continuous-and discrete-time neural network (NN) models has been investigated rather extensively. Concerning the design of associative memories, multistability of delayed hybrid NNs is studied in this paper with an emphasis on the impulse effects. Arising from the spiking phenomenon in biological networks, impulsive NNs provide an efficient model for synaptic interconnections among neurons. Using state-space decomposition, the coexistence of multiple equilibria of hybrid impulsive NNs is analyzed. Multistability criteria are then established regrading delayed hybrid impulsive neurodynamics, for which both the impulse effects on the convergence rate and the basins of attraction of the equilibria are discussed. Illustrative examples are given to verify the theoretical results and demonstrate an application to the design of associative memories. It is shown by an experimental example that delayed hybrid impulsive NNs have the advantages of high storage capacity and high fault tolerance when used for associative memories.

Exponential Synchronizationlike Criterion for State-Dependent Impulsive Dynamical Networks

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