Lag Synchronization Criteria Research Articles

Lag synchronization for coupled neural networks with multistate or multiderivative couplings

In this paper, two kinds of lag synchronization for coupled neural networks (CNNs) are addressed, that is, the cases with multiple state or derivative couplings. Firstly, several lag synchronization criteria for these two CNNs are derived by selecting proper state feedback controllers. Furthermore, since external disturbances in neural network implementation should not be ignored, the impact of external disturbances on the lag synchronization for CNNs are also further investigated. Lastly, the obtained criteria are verified through two illustrative examples.

Lag [formula omitted] synchronization and lag synchronization for multiple derivative coupled complex networks

This paper mainly devotes to the study of lag H∞ synchronization and lag synchronization issues for the multiple derivative coupled complex networks (MDCCNs) with and without external disturbances, which have never been investigated. On one side, with the help of state feedback controller, adaptive state feedback controller and Lyapunov functionals, two criteria are developed to insure the lag H∞ synchronization for the MDCCN with external disturbances. On the other side, we also discuss the lag synchronization in the MDCCN in virtue of choosing appropriate state feedback controller and adaptive state feedback controller. Lastly, two numerical examples are put forward to verify the lag H∞ synchronization and lag synchronization criteria.

Global projective lag synchronization of fractional order memristor based BAM neural networks with mixed time varying delays

AbstractThis paper addresses Master–Slave synchronization for some memristor‐based fractional‐order BAM neural networks (MFBNNs) with mixed time varying delays and switching jumps mismatch. Firstly, considering the inherent characteristic of FMNNs, a new type of fractional‐order differential inequality is proposed. Secondly, an adaptive switching control scheme is designed to realize the global projective lag synchronization goal of MFBNNs in the sense of Riemann‐Liouville derivative. Then, based on a suitable Lyapunov method, under the framework of set‐valued map, differential inclusions theory, fractional Barbalat's lemma and proposed control scheme, some new projective lag synchronization criteria for such MFBNNs are obtained. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed theoretical analysis.

Lag Exponential Synchronization of Delayed Memristor-Based Neural Networks via Robust Analysis

In this paper, the lag synchronization of delayed memristor-based neural networks (MBNNs) via robust analysis is studied. The MBNNs are neural networks closely related to the state variables. Therefore, the traditional linear feedback control may not achieve the goal of lag synchronization between the master system and the slave system. Under the definition of Filippov’s solution, we convert the varying weight coefficients of the MBNNs into interval perturbation which is the first time to consider positive real uncertainty and simultaneously avoid discussing the problem of parameter mismatch. Based on the Lyapunov–Krasovskii functional and an improved convex combination inequality, some new lag synchronization criteria are established in the form of linear matrix inequalities. Compared with some existing works, the robust analysis approach can improve the synchronization performance. Finally, numerical examples are provided to show the reliability and effectiveness of the results presented.

Generalized lag synchronization of multiple weighted complex networks with and without time delay

The generalized lag synchronization of multiple weighted complex dynamical networks with fixed and adaptive couplings is investigated in this paper, respectively. By designing appropriate controller, several synchronization criteria are presented for multiple weighted complex dynamical networks with and without time delay based on the selected Lyapunov functional and inequality techniques. Moreover, an adaptive scheme to update the coupling weights is also developed for ensuring the generalized lag synchronization of multiple weighted complex dynamical networks with and without time delay. Finally, two numerical examples are provided in order to validate effectiveness of the proposed generalized lag synchronization criteria.

Adaptive exponential lag synchronization for neural networks with mixed delays via intermittent control

In this paper, the problem of exponential lag synchronization for a class of neural networks with mixed delays including discrete and distributed delays is investigated via adaptive intermittent control. Based on piecewise analytic method, some sufficient conditions for globally exponential lag synchronization are established through constructing a piecewise continuous auxiliary function. It is noted that both the control periods and the control widths in our adaptive intermittent control strategy are allowed to be nonidentical, which extends the scope of application of periodically intermittent control with fixed both control period and control width employed widely in previous works. Moreover, it is shown that the derived globally exponential lag synchronization criteria are related to the control rates rather than the control periods, which facilitates the choice of the control periods for practical problems. Finally, a numerical example is given to illustrate the correctness of the obtained theoretical results.

Finite-time generalized projective lag synchronization criteria for neutral-type neural networks with delay

In this paper, we mainly investigate the finite-time generalized projective lag synchronization of neutral-type neural network with delay. With the help of the definition of finite-time generalized projective lag synchronization and Gronwall–Bellman inequality, the generalized projective lag synchronization is achieved between drive-response neural networks via a nonlinear feedback controller. Some novel and easily verifiable sufficient conditions are obtained. Many existing works can be regarded as special cases of our conclusions. Finally, we provide two simulation examples to verify the correctness of main results.

Finite-Time Lag Synchronization for Memristive Mixed Delays Neural Networks with Parameter Mismatch

This paper is devoted to study the finite time lag synchronization problem of memristive mixed delays neural networks with switching jumps and parameter mismatch. The main objective of this paper is to design simple linear feedback control such as the drive response systems can realize synchronization in the finite time. Several theoretical aspects are addressed, mean Filippov differential inclusion and set-valued map. Based on the Gronwall’s inequality and properties of differential operation, a new finite time lag synchronization scheme is proposed to guarantee that coupled memristive mixed delays neural networks are in a state of lag synchronization in finite time. In addition, finite lag synchronization criteria of two identical memristive mixed delays neural networks are also considered. Finally, numerical examples are presented to illustrate the effectiveness of the our proposed theorems.

Pinning lag synchronization of complex dynamical networks with known state time-delay and unknown channel time-delay

In this paper, a linear and adaptive feedback pinning strategy is used to study the lag synchronization of complex dynamical networks with known state time-delay and unknown channel time-delay. Firstly, based on the Lyapunov stability theory, a novel Lyapunov functional, which involves the estimated error $$\hat{e}_{i}(t)$$ rather than the general synchronization error $$e_{i}(t)$$ , is constructed. Secondly, in view of the unknown information of the channel time-delay, two available pinning controllers are designed such that the considered networks achieve lag synchronization. Furthermore, by a proper adaptation mechanism, we estimate the unknown channel time-delay successfully under the case that the initial value of the estimated channel time-delay is larger than true channel time-delay, i.e., $$\hat{\tau }(0)>\tau $$ and the another case $$\hat{\tau }(0)<\tau $$ . Finally, the effectiveness and correctness of the lag synchronization criteria are verified through two simulation experiments.

Finite-time lag synchronization of master-slave complex dynamical networks with unknown signal propagation delays

This paper studies the finite-time lag synchronization issue of master-slave complex networks with unknown signal propagation delays by the linear and adaptive error state feedback approaches. The unknown signal propagation delays are fully considered and estimated by adaptive laws. By designing new Lyapunov functional and discontinuous feedback controllers, which involves the estimated error rather than the general synchronization error, sufficient conditions are derived to ensure lag synchronization of the networks within a setting time. It is interesting to discover that the setting time is related to initial values of both the estimated error and the estimated unknown signal propagation delays. Finally, two numerical examples are given to illustrate the effectiveness and correctness of the proposed finite-time lag synchronization criteria.

Pinning lag synchronization of drive–response complex networks via intermittent control with two different switched periods

Abstract This paper develops an intermittent control with two switched periods to study the pinning lag synchronization problem of drive–response complex networks. These two switched periods may have different control rates. By designing appropriate adaptive intermittent pinning controllers and using Lyapunov stability theory, some sufficient conditions for ensuring the lag synchronization between two coupled networks are derived. The minimum number of pinned nodes is determined by node dynamics, coupling strength, inner coupling matrix and a design parameter. Two simple pinning lag synchronization criteria are obtained from the proposed conditions. A numerical example is provided to illustrate the feasibility of the theoretical results.

Pinning synchronization of the drive and response dynamical networks with lag

Abstract This paper investigates the pinning synchronization of two general complex dynamical networks with lag. The coupling configuration matrices in the two networks are not need to be symmetric or irreducible. Several convenient and useful criteria for lag synchronization are obtained based on the lemma of Schur complement and the Lyapunov stability theory. Especially, the minimum number of controllers in pinning control can be easily obtained. At last, numerical simulations are provided to verify the effectiveness of the criteria

Adaptive generalized function matrix projective lag synchronization between fractional-order and integer-order complex networks with delayed coupling and different dimensions

This paper investigates generalized function matrix projective lag synchronization between fractional-order and integer-order complex networks with delayed coupling, non-identical topological structures and different dimensions. Based on Lyapunov stability theory, generalized function matrix projective lag synchronization criteria are derived by using the adaptive control method. In addition, the three-dimensional fractional-order chaotic system and the four-dimensional integer-order hyperchaotic system as the nodes of the drive and the response networks, respectively, are analyzed in detail, and numerical simulation results are presented to illustrate the effectiveness of the theoretical results.

Observer-based lag synchronization between two different complex networks

In this paper, some new criteria for lag synchronization between two or more complex networks are proposed based on the theory of state observer. Some adaptive controllers are designed to make the drive and response systems achieve lag synchronization, no matter whether the nodes in the two systems are with the same dynamical character or the coupling configuration matrices are nonidentical. In addition, based on the output coupling, the amount of coupling variables between two connected nodes is flexible, which can save a lot of channel resources, simplify the network topology and has more significant meanings in engineering applications. At last, the effects of the lag synchronization criteria are verified through some simulation experiments.

Adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions

The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory and Barbalat's lemma, generalized matrix projective lag synchronization criteria are derived by using the adaptive control method. Furthermore, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. In addition, numerical simulation results are presented to illustrate the effectiveness of this method, showing that the synchronization speed is sensitively influenced by the adaptive law strength, the network size, and the network topological structure.

Some new criteria for lag synchronization of chaotic Lur'e systems by replacing variables control

Some new criteria for the chaotic lag synchronization are proposed. At first,lag synchronization scheme for identical master-slave Lur‘ e systems by replacing variables control and the relevant error system are given, and the relations between absolute stability of the error system and the chaotic lag synchronization are described. Then, based on a quadratic Lyapunov function, two new Lur‘ e criteria for the above chaotic lag synchronization are proved. Four corresponding frequency domain criteria are further derived by means of Meyer-Kalman-Yacubovia Lemma. These frequency domain criteria are applied to analyze the lag synchronization of general master-slave Chua's circuits so that some ranges of the parameters in which the master-slave Chua's circuits achieve chaotic lag synchronization by replacing single-variable control are attained. Finally, some examples are given to verify the theoretical results.