Criteria For Global Synchronization Research Articles

Synchronization control of quaternion‐valued inertial memristor‐based neural networks via adaptive method

In this paper, by introducing memristive connections and inertial term into quaternion‐valued neural networks, the quaternion‐valued inertial memristive neural networks (QVIMNNs) is proposed. Based on the adaptive control strategy, the synchronization problem of the QVIMNNs is analyzed in this work. Two different assumption for activation functions are considered in this work; new criteria for global synchronization are then derived by designing novel adaptive controllers and update laws. Lastly, numerical examples are given to verify the results obtained in this work.

Exponential synchronization of quaternion‐valued memristor‐based neural networks with time‐varying delays

SummaryIn this paper, the global exponential synchronization of quaternion‐valued memristor‐based neural networks with time‐varying delays is discussed. Firstly, by using the differential inclusion theory and the set‐valued map theory, the discontinuous quaternion‐valued memristive neural networks is transformed into an uncertain system with interval parameters. A novel controller is designed to achieve the control goal. With the ‐measure method and Halanay inequality, the criterion for global exponential synchronization of the quaternion‐valued memristive neural networks is given. At last, a numerical simulation is given to prove the validity of the main results.

Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under effective impulse macroeconomic management means. Matlab’s LMI toolbox is utilized to deduce the feasible solution in a numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

An asymptotic state estimator design and synchronization criteria for fractional order time‐delayed genetic regulatory networks

AbstractThis paper mainly investigates the asymptotic state estimator design and impulsive controlled synchronization for fractional‐order time‐delayed genetic regulatory networks (FOTDGRNs). Different from the existing state estimator results, the asymptotic state estimator design of FOTDGRNs is studied by using a novel algebraic method, fractional‐order Lyapunov–Razumikhin method, and some famous inequality techniques. Afterward, a suitable impulsive controller is designed for the global asymptotic synchronization criteria for addressing master–slave systems. At last, the paper comes up with two numerical cases to justify the applicability of our theoretical outcomes.

Global dissipativity and adaptive synchronization for fractional‐order time‐delayed genetic regulatory networks

AbstractThis manuscript examines global dissipativity and synchronization criteria for time‐delayed fractional‐order gene regulatory networks (FGRNs). The Lyapunov stability theory is used to examine a class of FGRNs with delay arguments that are inspired by the integer‐order delayed gene regulatory network model. Some sufficient criteria are established using the fractional‐order comparison principle and stability theorem for fractional‐order time‐delayed systems to ensure the global dissipativity solution of FGRNs with both feedback regulation and translation time delays. Furthermore, for FGRNs, the global asymptotic synchronization condition is accomplished by constructing an adaptive delayed feedback control method for the master–slave system. Finally, two numerical examples are provided to demonstrate the applicability and superiority of the conclusions obtained.

Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays

In this paper, the synchronization control problem of high-order quaternion Hopfield neural networks (HOQHNNs) with unbounded distributed delays and time-varying discrete delays is studied. Since the non-exchangeability of quaternion multiplication operation, the error system is first decomposed into equivalent real-valued systems, and then the driving-response structure of HOQHNN is achieved exponential synchronization by designing a state feedback controller. At the same time, two examples are offered to illustrate the applicability of the consequences obtained. Finally, the obtained global exponential synchronization criterion is applied to encrypt and decrypt color images. The method proposed here has four advantages: (1) There is no need to construct any Lyapunov–Krasovskii functional, which is straight in the light of the definition of global exponential synchronization; (2) The obtained synchronization criterion contains only a few simple inequalities, which can find the solutions readily; (3) The proposed method is available to real-valued and complex-valued neural networks; (4) The obtained results are helpful for the image secure transmission.

Global synchronization of uncertain fractional-order BAM neural networks with time delay via improved fractional-order integral inequality

This paper is concerned with the problem of global synchronization for a class of uncertain fractional-order bidirectional associative memory (FOBAM) neural networks (NNs) with constant time delay. Some linear matrix inequality (LMI) based conditions have been established for ensuring the stability behavior of the governing augmented system derived from the considered fractional-order master system and the constructed slave system. In such LMI conditions, for utilizing the information on the time delay terms and the order of the fractional derivative, some fractional-order integral inequalities have been developed. Next, by defining a new Lyapunov–Krasovskii functional (LKF) and based on the improved fractional-order inequalities, the global synchronization criteria have been established in terms of a solvable set of LMIs for the considered class of uncertain FOBAM NNs without uncertain matrices. Further, the obtained results have been extended to the case of uncertain FOBAM NNs. Finally, a numerical example is presented to illustrate the feasibility and effectiveness of the proposed theoretical results.

Pinning Impulsive Synchronization of Complex Networks with Multiple Sizes of Delays via Adaptive Impulsive Intervals

The leader-following issue for a class of nonlinearly coupled complex networks with multiple time-varying delays was investigated in this study. A distributed controller was introduced for realizing the exponential synchronization of the complex network with different delay scales that are known in advance. The Lyapunov stability theorem and mathematical induction method were used to obtain delay-dependent criteria for global impulsive synchronization. Additionally, an adaptive strategy was adopted to establish appropriate impulsive intervals suitable for various delays. The fact that the proposed adaptive scheme is more general and less conservative enables the effective release of the constriction caused by unknown delay scales. Furthermore, the pinning impulsive control method enables the control cost to be further reduced. Finally, several numerical simulations were performed to evaluate the effectiveness of the mathematical deductions.

Global exponential synchronization via nonlinear feedback control for delayed inertial memristor-based quaternion-valued neural networks with impulses

The issue of global exponential synchronization is addressed for delayed impulsive and time-varying delayed inertial memristor-based quaternion-valued neural networks (IMQVNNs). First, the concept of the Filippov solution for IMQVNNs is introduced by applying differential inclusion theory. Then, a nonlinear feedback controller is designed in the skew field of quaternions to ensure the realization of global exponential synchronization for IMQVNNs. According to this controller, the global exponential synchronization criteria are established based on the Lyapunov stability theory. Moreover, a corollary for the real-valued system is given to compare with the existing conclusions. Finally, two examples are presented to show the validity of the results.

The global finite-time synchronization of a class of chaotic systems via the variable-substitution and feedback control

AbstractThis paper deals with the global finite-time synchronization of a class of third-order chaotic systems with some intersecting nonlinearities, which cover many famous chaotic systems. First, a simple, continuous and dimension-reducible control by the name of the variable-substitution and feedback control is designed to construct a master–slave finite-time synchronization scheme. Then, a global finite-time synchronization criterion for the synchronization scheme is proven and the synchronization time is analytically estimated. Subsequently, the criterion and optimization technique are applied to the well-known brushless direct current motor (BLDCM) system and the classic Lorenz system, respectively, further obtaining some new optimized synchronization criteria in the form of algebra. Two numerical examples for the BLDCM system and a numerical example for the Lorenz system are simulated and analyzed to verify the effectiveness of the theoretical results obtained in this paper.

Global synchronization of coupled delayed memristive reaction–diffusion neural networks

This paper focuses on the global exponential synchronization of multiple memristive reaction–diffusion neural networks (MRDNNs) with time delay. Due to introducing the influences of space as well as time on state variables and replacing resistors with memristors in circuit realization, the state-dependent partial differential mathematical model of MRDNN is more general and realistic than traditional neural network model. Based on Lyapunov functional theory, Divergence theorem and inequality techniques, global exponential synchronization criteria of coupled delayed MRDNNs are derived via directed and undirected nonlinear coupling. Finally, three numerical simulation examples are presented to verify the feasibility of our main results.

Pinning synchronization of weighted bipartite networks with time-varying delays via aperiodic intermittent control

Bipartivity has been revealed as an important topological feature of many real networks. In this paper, we first propose a model of weighted bipartite networks with time-varying delays, where both internal delay and communication delay are incorporated, and meanwhile the delayed coupling contains only one single transmittal delay. Then we investigate its pinning synchronization problem via aperiodic intermittent control. By utilizing the Lyapunov functional method and mathematical induction, a generic global exponential synchronization criterion is established. Moreover, based on the theory of linear algebra, two easy verifiable low-dimensional synchronization conditions are obtained. It is shown that the network nodes with the highest degrees should be pinned successively. Finally, numerical simulations are given to verify the validity of the theoretical analysis.

Global power synchronization of complex dynamical networks with proportional delay and impulsive effects

This paper discusses the global power synchronization of a class of coupled neural networks with proportional delay and impulsive effects. By constructing Lyapunov functionals and introducing a new concept named “log average impulsive interval”, a unified global power synchronization criterion is derived for the addressed impulsive complex networks, which is simultaneously effective for synchronizing impulses and desynchronizing impulses. Based on a known impulsive delay inequality involving proportional delay, suitable impulsive controllers are also designed to globally power synchronize complex dynamical networks with proportional delay. The conditions are represented as linear matrix inequalities, and so they are convenient and feasible in practical problems. Two illustrative numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Global asymptotic synchronization of impulsive fractional-order complex-valued memristor-based neural networks with time varying delays

This paper investigates the global synchronization of impulsive fractional-order complex-valued memristor-based neural networks with time varying delays. Based on the Riemann-Liouville (R-L) derivative, by applying Lyapunov functional approach and using the comparison theorem, we derive some global synchronization criteria for the fractional order linear systems. Global asymptotic synchronization criteria are achieved through the employment of a pinning control and comparison theorem of fractional order systems. Finally, the effectiveness of the proposed method is validated through a constructive numerical example.

Global synchronization of time-invariant uncertainty fractional-order neural networks with time delay

This paper considers the global synchronization problem of time-invariant uncertainty fractional-order neural networks with time delay. First, the time-invariant uncertain items are converted into the positive real uncertainties. Then, in order to deal with time delay terms, a novel free-matrix-based fractional-order integral inequality (FMBFII) is proposed by using the fractional-order Leibniz–Newton formula and a new class of Lyapunov–Krasovskii functions is constructed. Next, based on FMBFII, Lyapunov–Krasovskii functions and fractional-order integral Jensen’s inequality, several global synchronization criteria for time-invariant uncertainty fractional-order neural networks with time delay are studied. Furthermore, compared to the previous fractional-order integral Jensen’s inequality, the advantage of the proposed FMBFII is theoretically analyzed. Finally, by using two examples, the feasibility and effectiveness of our proposed results are tested.

Stability and synchronization criteria for fractional order competitive neural networks with time delays: An asymptotic expansion of Mittag Leffler function

Competitive neural networks(CNNs) has not been well developed in nonlinear fractional order dynamical system, which is developed first time in this paper. Then, by means of a proper Lyapunov functional, asymptotic expansion of Mittag-Leffler function properties, together with some Caputo derivative properties, the testable novel sufficient conditions are given to guarantee the existence, uniqueness of the equilibrium point as well as global asymptotic stability for a class of fractional order competitive neural networks (FOCNNs) are all derived in the form of matrix elements. Furthermore, the boundedness for the solution of FOCNN is presented by employing Cauchy–Schwartz inequality and Gronwall inequality. Besides, a linear feedback control and adaptive feedback control are designed to achieve the global asymptotic synchronization criterion for FOCNNs with time delay and these explored consequences are extended from some previous integer order CNNs output. At last, two numerical simulations are performed to illustrate the effectiveness of our proposed theoretical results.

Aperiodic intermittent pinning control for exponential synchronization of memristive neural networks with time-varying delays

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.

Synchronization Analysis of Two-Time-Scale Nonlinear Complex Networks With Time-Scale-Dependent Coupling.

In this paper, a time-scale-dependent coupling scheme for two-time-scale nonlinear complex networks is proposed. According to this scheme, the inner coupling matrices are related to the fast dynamics of individual subsystems, but are no longer time-scale-independent. Designing time-scale-dependent inner coupling matrices is motivated by the fact that the difference of time scales is an essential feature of modular architecture of two-time-scale systems. Under the novel coupling framework, the previous assumption on individual two-time-scale subsystems that the fast dynamics must be exponentially stable can be removed. The idea of time-scale separation is employed to analyze the stability of synchronization error systems via weighted ε -dependent Lyapunov functions. For a given upper bound of the singular perturbation parameter ε , it is proved that the exponential decay rate of the synchronization error can be guaranteed to be independent of the value of ε . In this way, criteria for local and global exponential synchronization are established. The allowable upper bound of ε such that the synchronizability of the considered two-time-scale network is retained can be obtained by solving a set of ε -dependent matrix inequalities. Finally, the efficiency of the proposed time-scale-dependent coupling strategy is demonstrated through numerical simulations.

Generalized pinning synchronization of delayed Cohen–Grossberg neural networks with discontinuous activations

In this article, generalized pinning synchronization problem is investigated for a class of Cohen–Grossberg neural networks with discontinuous neuron activations and mixed delays. By designing generalized pinning state-feedback and adaptive controllers, several criteria for global exponential synchronization and global asymptotical synchronization of the drive–response based system are obtained in view of non-smooth analysis theory with generalized Lyapunov functional method, in which first pinning the neurons with very small self-inhibition and small amplification functions is pointed out. Some numerical examples are given to illustrate the feasibility of the obtained results.

Adaptive Synchronization of Fractional Order Complex-Variable Dynamical Networks via Pinning Control**Supported by National Natural Science Foundation of China under Grant No. 61201227, National Natural Science Foundation of China Guangdong Joint Fund under Grant No. U1201255, the Natural Science Foundation of Anhui Province under Grant No. 1208085MF93, 211 Innovation Team of Anhui University under Grant Nos. KJTD007A and KJTD001B, and also

In this paper, the synchronization of fractional order complex-variable dynamical networks is studied using an adaptive pinning control strategy based on close center degree. Some effective criteria for global synchronization of fractional order complex-variable dynamical networks are derived based on the Lyapunov stability theory. From the theoretical analysis, one concludes that under appropriate conditions, the complex-variable dynamical networks can realize the global synchronization by using the proper adaptive pinning control method. Meanwhile, we succeed in solving the problem about how much coupling strength should be applied to ensure the synchronization of the fractional order complex networks. Therefore, compared with the existing results, the synchronization method in this paper is more general and convenient. This result extends the synchronization condition of the real-variable dynamical networks to the complex-valued field, which makes our research more practical. Finally, two simulation examples show that the derived theoretical results are valid and the proposed adaptive pinning method is effective.