Robust synchronization of uncertain chaotic systems

This paper investigates robust unified (lag, anticipated, and complete) synchronization of two coupled chaotic systems. By introducing the concepts of positive definite symmetrical matrix and Riccati inequality and the theory of robust stability, several criteria on robust synchronization are established. Extensive numerical simulations are also used to confirm the results.     

Study on Proportional Synchronization of Hyperchaotic Circuit System

In this paper, the proportional synchronization between drive system and response system is achieved by using the concept of generalized synchronization. The phase space of all variables in response system can be expanded and compressed flexibly. Meanwhile, the 6-D hyperchaotic chua's circuit is considered as an illustrative example to demonstrate the effectiveness of the proposed approach. Furthermore, focusing on the shortcoming of the long transient behavior during the process of synchronization, a feedback method is adopted to shorten the transitional time of synchronization, which will provide an effective way for speeding up the transmitting velocity of code in chaotic multiple access communication.     

Adaptive generalized functional synchronization of chaotic systems with unknown parameters

A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class of chaotic system. Self-adaptive parameter law and control law are given in the form of a theorem. The synchronization between the three-dimensional R6ssler chaotic system and the four-dimensional Chen＇s hyper-chaotic system is studied as an example for illustration. The computer simulation results demonstrate the feasibility of the method proposed.     

两个不相同系统的广义同步化

采用Temam无穷维动力系统的惯性流形理论，证明了两个不相同的系统能实现广义同步化.在两个系统具有吸收集和吸引子的基础上，通过定义在一个函数类上的压缩映射的不动点得到了广义同步化流形，该流形是Lipschitz光滑流形，而且具有不变性与指数吸引性.数值仿真证实了所建立理论的正确性.     

Experimental observation of direct current voltage-induced phase synchronization

The dynamics of two uncoupled distinct Chua circuits driven by a common direct current voltage is explored experimentally. It was found that, with increasing current intensity, the dominant frequencies of these two Chua circuits will first vary at different speeds, approach an identical value for a certain current intensity and then separate. Techniques such as synchronization index and phase difference distribution were employed to analyze the phase coherence between these two Chua circuits.     

强耦合混沌系统中的近似同步

以单向驱动耦合Lorenz振子一维链为研究对象，研究振子间的混沌同步行为. 数值计算结果表明，对于变量y驱动x的耦合方式，在合适的耦合强度下，会出现第一个振子和第二个振子不同步，而与次近邻非直接连接的振子(如第三个振子)近似同步. 进一步研究表明，出现这一现象的原因是在大耦合强度下，对于这种驱动方式，第一个振子和第二个振子间出现驱动单变量近似同步；虽然它们之间未出现所有变量的完全同步，但是驱动信号事实上已经传递下去了. 关键词： Lorenz振子 混沌同步 近似同步     

广义混沌同步中的多稳定同步流形

从构造驱动系统和响应系统之间的函数关系出发,一般性地研究了广义混沌同步中同步流形的多值性问题,并对同步流形的稳定性进行了分析,提出了多稳定同步流形存在的条件.利用该稳定性条件对两个实例进行了分析,一个为Genesio-Rssler耦合系统,另一个为具有二次、三次非线性的耦合Duffing系统,结果表明前者仅有唯一的稳定同步流形,而后者随着耦合强度的增加,从具有两个稳定的同步流形变为只存在一个稳定同步流形. 关键词： 混沌同步 多稳定性 同步流形     

Adaptive synchronization of uncertain chaotic systems via switching mechanism

This paper deals with the problem of synchronization for a class of uncertain chaotic systems.The uncertainties under consideration are assumed to be Lipschitz-like nonlinearity in tracking error,with unknown growth rate.A logic-based switching mechanism is presented for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system.Based on the Lyapunov approach,the adaptation law is determined to tune the controller gain vector online according to the possible nonlinearities.To demonstrate the efficiency of the proposed scheme,the well-known chaotic system namely Chua’s circuit is considered as an illustrative example.     

Reliable impulsive synchronization for a class of nonlinear chaotic systems

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

研究多中心奇异吸引子混沌相位的新方法

对一般混沌轨迹的相位定义进行了研究,考虑到大量的混沌运动投影到相平面后不是只有一个转动中心的正规转动,给出了两种计算瞬时相位的简单方法.一种方法称之为直接分解方法,它是基于分解的思想.另一种是切线方法,它需要计算轨迹在切空间中的角度.通过对一些算例结果的比较,可以看出这两种方法的优越性.综合而言,切线方法是对任意混沌振动适用的,因此可以被广泛应用于混沌相位同步的研究中 关键词： 混沌同步 相位同步 正规转动     

一类分数阶混沌系统的自适应同步

针对一类分数阶混沌系统的同步问题,基于分数阶系统的类Lyapunov稳定性理论,设计了一种新的自适应同步控制器以及控制增益系数自适应律.与现有结果相比,该方法具有控制器结构简单、控制代价小以及通用性强等特点,可适用于大部分典型的分数阶混沌系统.最后,数值仿真结果验证了所提方法运用于分数阶混沌系统同步研究的有效性.     

Controlling projective synchronization in coupled chaotic systems

In this paper, a new method for controlling projective synchronization in coupled chaotic systems is presented. The control method is based on a partially linear decomposition and negative feedback of state errors. Firstly, the synchronizability of the proposed projective synchronization control method is proved mathematically. Then, three different representative examples are discussed to verify the correctness and effectiveness of the proposed control method.     

Segmented Spiral Waves and Anti-phase Synchronization in a Model System with Two Identical Time-Delayed Coupled Layers

In this paper, we consider a model system with two identical time-delayed coupled layers. Synchronization and anti-phase synchronization are exhibited in the reactive system without diffusion term. New segmented spiral waves, which are constituted by many thin trips, are found in each layer of two identical time-delayed coupled layers, and are different from the segmented spiral waves in a water-in-oil aerosol sodium bis（2-ethylhexyl） sulfosuccinate （AOT） microemulsion （ME） （BZ-AOT system）, which consists of many small segments. ＂Anti-phase spiral wave synchronization＂ can be realized between the first layer and the second one. For different excitable parameters, we also give the minimum values of the coupling strength to generate segmented spiral waves and the tip orbits of spiral waves in the whole bilayer.     

Lorenz系统族采样同步研究

从对连续时间混沌系统进行数字测量的角度，提出了连续时间混沌系统的采样同步问题. 利用控制理论的结果，设计了Lorenz系统族的采样同步系统. 仅需测量一个状态分量，就可在采样时刻实现同步. 数值模拟例证了同步的性能. 关键词： 混沌同步 Lorenz系统族 采样同步     

On multi switching compound synchronization of non identical chaotic systems

Multi switching compound synchronization (MSCOS) between four non identical chaotic systems is investigated. Chen system is considered as scaling drive system. Lorenz and Lü systems are taken as base drive systems. The compound of the multi drive system is then synchronized with Rössler response system using multi switching synchronization scheme. In MSCOS, the state variables of three drive systems synchronize with different state variables of response system, simultaneously. For suitable choice of scaling factors, switched modified function projective synchronization is obtained as a special case of MSCOS among chaotic systems. To achieve the desired synchronization among four non identical chaotic systems, sufficient condition is obtained using a nonlinear controller and Lyapunov stability theory, and corresponding theoretical proofs are given. The effectiveness of the proposed controllers is verified by numerical simulations using MATLAB.     

A function cascade synchronization method with unknown parameters and applications

This paper investigates the function cascade synchronization of chaos system. Combining cascade synchronization scheme, parametric adaptive control and projective synchronization scheme, it proposes a new function cascade synchronization scheme to address a generalized-type synchronization problem of three famous chaotic systems: the Lorenz system, Liu system and R\"{o}ssler system, the states of two identical chaotic systems with unknown parameters can be asymptotically synchronized by choosing different special suitable error functions. Numerical simulations are used to verify the effectiveness of the proposed synchronization techniques.     

A function cascade synchronization method with unknown parameters and applications

This paper investigates the function cascade synchronization of chaos system. Combining cascade synchronization scheme, parametric adaptive control and projective synchronization scheme, it proposes a new function cascade synchronization scheme to address a generalized-type synchronization problem of three famous chaotic systems： the Lorenz system, Liu system and RSssler system, the states of two identical chaotic systems with unknown parameters can be asymptotically synchronized by choosing different special suitable error functions. Numerical simulations are used to verify the effectiveness of the proposed synchronization techniques.     

长距离多站点高精度光纤时间同步

为了保证长距离多站点间的高精度时间同步,在利用双向时间比对法实现高精度长距离时间同步的基础上,提出了一种利用一个波长信道同时对1 PPS(pluse per second)信号、时码信号以及10 MHz信号进行传递,并使用时分多址和净化再生的方式实现多站点高精度光纤时间同步的方法.以自行研制的工程样机在长度约550 km的实验室光纤链路以及871.6 km的实地光纤链路上进行了实验验证.在实验室光纤链路上,同时在50,300,550 km处测量得到的时间同步标准差分别为16.7,16.8,18.4 ps,时间稳定度分别为1.78 ps@1000 s,2.09 ps@1000 s,2.92 ps@1000 s.在实地光纤链路上,实现了光纤链路沿途11个站点的时间同步,测得871.6 km传递链路的时间同步标准差为29.8 ps,时间稳定度为3.85 ps@1000 s,不确定度为25.4 ps.     

Phase synchronization and its transition in two coupled bursting neurons: theoretical and numerical analysis

It is crucially important to study different synchronous regimes in coupled neurons because different regimes may correspond to different cognitive and pathological states. In this paper, phase synchronization and its transitions are discussed by means of theoretical and numerical analyses. In two coupled modified Morris--Lecar neurons with a gap junction, we show that the occurrence of phase synchronization can be investigated from the dynamics of phase equation, and the analytical synchronization condition is derived. By defining the phase of spike and burst, the transitions from burst synchronization to spike synchronization and then toward nearly complete synchronization can be identified by bifurcation diagrams, the mean frequency difference and time series of neurons. The simulation results suggest that the synchronization of bursting activity is a multi-time-scale phenomenon and the phase synchronization deduced by the phase equation is actually spike synchronization.     

基于函数矩阵的一类混沌系统同步

研究了一类混沌系统的同步问题、基于稳定性理论和极点配置技术,设计了两个混沌系统之间的同步方案,实现两个混沌系统之间的同步,通过函数矩阵,实现驱动系统和响应系统的状态变量按给定的函数矩阵同步,同时证明了该方法同样适用于两个混沌系统之间的滞后同步,通过对Lorenz混沌系统和Lorenz超混沌系统的数值模拟,进一步验证了所提方案的有效性。