Lag quasisynchronization of coupled delayed systems with parameter mismatch by periodically intermittent control

This paper further investigates the lag synchronization of coupled delayed systems with parameter mismatch. Different from the most existing results, we formulate the intermittent control system that governs the dynamics of the synchronization error. As a result of parameter mismatch, complete lag synchronization cannot be achieved. In this paper, a lag quasisynchronization scheme is proposed to ensure that coupled systems are in a state of lag synchronization with an error level. We estimate the error bound of lag synchronization by rigorously theoretical analysis. Numerical simulations are presented to verify the theoretical results.     

Lag synchronization for fuzzy chaotic system based on fuzzy observer

A new fuzzy observer for lag synchronization is given in this paper. By investi- gating synchronization of chaotic systems, the structure of drive-response lag synchronization for fuzzy chaos system based on fuzzy observer is proposed. A new lag synchronization criterion is derived using the Lyapunov stability theorem, in which control gains are obtained under the LMI condition. The proposed approach is applied to the well-known Chen＇s systems. A simulation example is presented to illustrate its effectiveness.     

Adaptive lag synchronization in coupled chaotic systems with unidirectional delay feedback

Lag synchronization in unidirectionally coupled chaotic systems is investigated in this paper. Based on the invariance principle of differential equations, a new adaptive delay feedback scheme is proposed to realize the lag synchronization effectively in the coupled chaotic systems. As an example, numerical simulations for the coupled Hindmarsh-Rose (HR) neuron models are conducted, which is in good agreement with the theoretical analysis. More interestingly, it is found that there is a fine U-shaped structure in the lag synchronization curve for the HR neuron model. Furthermore, lag synchronization and the corresponding U-shaped structure are robust against the small mismatch of parameters and noisy disturbances.     

Influence of the time delay of signal transmission on synchronization conditions in drive-response systems

Conditions for complete and lag synchronizations in drive-response systems are considered under the unified framework of generalized synchronization. The question is addressed that whether the synchronization conditions achieving complete synchronization is still valid for lag synchronization when the time delay of signal transmission between the drive and response systems increases from 0. Theoretical and numerical results show that whether the synchronization conditions is stable for the influence of the time delay of signal transmission depends on a particular form of equilibria of the drive and response systems. Furthermore, it seems that the less the number of the equilibria of the drive system, the more likely the synchronization conditions are stable for the time delay of signal transmission.     

Projectively lag synchronization and uncertain parameters identification of a new hyperchaotic system

This paper investigates projectively lag synchronization of a new hyperchaotic system (proposed by Yang et al. in Nonlinear Anal., Real World Appl., 10:1601, 2009), with certain/uncertain parameters. Based on the Lyapunov function constructing method and application of the Babarǎt lemma, projectively lag synchronization is achieved for the new hyperchaotic system by designing nonlinear controllers. Furthermore, a novel method is proposed to identify unknown parameters based on projectively lag synchronization of the new hyperchaotic system. Finally, several numerical simulations are given to verify and test the correctness and effectiveness of the novel methods we proposed.     

Reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems

The problem of reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems is investigated in this paper. Firstly a reliable impulsive controller is designed by the impulsive control theory. Then, some sufficient conditions for reliable impulsive lag synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.     

Lag synchronization between discrete chaotic systems with diverse structure

A lag synchronization controller is designed in studying discrete chaotic systems with diverse structures to realize synchronization between Henon and Ikeda sys- terns. The structure of the lag synchronization controller and the error equations of state variables between discrete chaotic systems are presented based on the stability theory. The designed controller has unique structures for different chaotic systems. Lag synchro- nization between any discrete chaotic systems with diverse structures can be achieved. Simulation results show that this control method is effective and feasible.     

Projective and lag synchronization between general complex networks via impulsive control

This paper mainly investigates the projective and lag synchronization between general complex networks via impulsive control. A general drive complex network and an impulsively controlled slave network are presented in the model. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. Some criteria and corollaries are, respectively, derived for the projective synchronization and lag synchronization between the presented impulsively controlled complex networks. Finally, the results are illustrated by complex networks composed of the chaotic Lorenz systems. All the numerical simulations verify the correctness of the theoretical results.     

A kind of binary scaling function projective lag synchronization of chaotic systems with stochastic perturbation

This paper investigates a kind of binary function projective lag synchronization of uncertain chaotic systems with stochastic perturbation. In comparison with those of the existing scaling function synchronization, we assume that the given scaling function can be the binary boundary function, even an n-ary boundary function. Based on the LaSalle-type invariance principle for stochastic differential equation, the adaptive control law is derived to make the state of two chaotic systems function projective lag synchronized. Some numerical is also given to show the effectiveness of the proposed method.     

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.     

Generalized heterochronous synchronization in coupled time-delayed chaotic systems

A new kind of generalized heterochronous synchronization phenomenon is reported. Different kinds of generalized synchronous states (including generalized anticipated, isochronous and lag projective synchronization) coexist among different state variables between two unidirectionally coupled time-delayed chaotic systems. The analytical conditions for generalized heterochronous synchronization are obtained. We also find that the synchronization conditions are independent of the delay times in the original time-delayed system. The theoretical results are well confirmed by the numerical simulations and electronic circuit experiments.     

Hybrid robust modified function projective lag synchronization in two different dimensional chaotic systems

In this article, a novel synchronization scheme, modified function projective lag synchronization (MFPLS) in two different dimensional chaotic systems with parameter perturbations, is proposed. In the proposed method, the states of two nonidentical chaotic systems with different orders are asymptotically lag synchronized up to a desired scaling function matrix by means of reduced order and increased order, respectively. Furthermore, based on the reality situation, the parameter perturbations are involved, which are assumed to appear in both drive and response systems. With the Lyapunov stability theory, an adaptive controller is designed to achieve MFPLS. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.     

Modified function lag projective synchronization of a financial hyperchaotic system

This paper presents a new type synchronization called modified function lag projective synchronization (MFLPS), where the drive and response systems could be synchronized up to a desired scale function matrix with time-delay. With MFLPS it achieves self-synchronization of a financial hyperchaotic system when the parameters are known and unknown, respectively. The corresponding numerical simulations are performed to verify and illustrate the analytical results.     

Successive lag synchronization on nonlinear dynamical networks via aperiodically intermittent control

Nonlinear Dynamics - Successive lag synchronization (SLS) for nonlinear dynamical networks is investigated by using aperiodically intermittent control. Different from previous works about the SLS,...     

Sampled-data-based lag synchronization of chaotic delayed neural networks with impulsive control

Nonlinear Dynamics - In the framework of sampled-data control, this paper deals with the lag synchronization of chaotic neural networks with time delay meanwhile taking the impulsive control into...     

Anticipatory, complete and lag synchronization of chaos and hyperchaos in a nonlinear delay-coupled time-delayed system

We study the synchronization of chaos and hyperchaos in first-order time-delayed systems that are coupled using the nonlinear time-delay excitatory coupling. We assign two characteristic time delays: the system delay that is same for both the systems, and the coupling delay associated with the coupling path. We show that depending upon the relative values of the system delay and the coupling delay the coupled systems show anticipatory, complete, and lag synchronization. We derive a general stability condition for all the synchronization processes using the Krasovskii–Lyapunov theory. Numerical simulations are carried out to corroborate the analytical results. We compute a quantitative measure to ensure the occurrence of different synchronization phenomena. Finally, we set up an experiment in electronic circuit to verify all the synchronization scenario. It is observed that the experimental results are in good agreement with our analytical results and numerical observations.     

Secure communication using chaotic synchronization in mutually coupled semiconductor lasers

In this paper, we propose a scheme of the secure communication systems, in the frame of the chaotic synchronization of two semiconductor lasers with optical feedback in mutually coupled configuration within the new modified rate equation of lasers by using the numerical simulations. We explore the robustness of this synchronization scheme with parameter mismatches. A high sensitivity of the synchronization of the lasers via the new control parameter mismatch is discussed in the temporal and frequency domains. Moreover, a possible complete synchronization with negative time lag is discussed. As a result, this leads the receiver to be in the future state of the transmitter. To sustain this proposed scheme, we present the encrypted transmission of binary messages at a bit rate of 250?Mbits/s, and we show that the digital messages at the output receiver laser are perfectly recovered using a finite impulse response filter. The error bits, the error rates as well as the effects of parameter mismatches on the recovered messages are evaluated.     

Lag synchronization of hyperchaotic complex nonlinear systems

In this paper, we study the lag synchronization (LS) of n-dimensional hyperchaotic complex nonlinear systems. The idea of the nonlinear control technique based on the complex Lyapunov function with lag in time is used to propose a scheme to investigate LS of hyperchaotic attractors of these systems. Both complex Lyapunov and control functions are introduced. For illustration, the scheme is applied to two hyperchaotic complex Lorenz systems. The real and complex control functions are derived analytically to achieve LS and to show that the complex error dynamical systems are globally stable. Numerical results are calculated to test the validity of the analytical expressions of control functions to achieve LS of two identical hyperchaotic attractors.     

Adaptive generalized function matrix projective lag synchronization of uncertain complex dynamical networks with different dimensions

Generalized function matrix projective lag synchronization of uncertain complex dynamical networks with different dimension of nodes via adaptive control method is investigated in this paper. Based on Lyapunov stability theory, adaptive controller is obtained and unknown parameters of both the drive network and the response network are estimated by adaptive laws. In addition, the three-dimension chaotic system and the four-dimension hyperchaotic system, respectively, as the nodes of the drive and response network are analyzed in detail, and numerical simulation results are presented to illustrate the effectiveness of the theoretical results.     

畸变信号的反演修正在同步测压中的应用

本文说明了同步测压所包含的主要内容以及一套实用的同步测压系统的组成，分析了通过传压管道传递的压力信号产生畸变的原因，指出对畸变信号进行反演修正是同步测压过程中必不可少的关键环节。利用频域修正的方法可以对压力分布同步测量中的畸变信号进行反演，以消除输出信号的幅值误差和相位差，保证各个测压通道得到的信号在时间上具有良好的同步性。这样就可以通过对脉动压力分布进行面积加权积分，得到脉动气动力的时间历程。在对畸变信号进行反演修正时，得到测压系统的频率响应函数是关键，本文介绍了利用比较法来标定频响曲线的装置和方法。并通过实验演示了反演修正的效果，表明本文所采用的同步测压装置具有非常好的同步性能。