Projective synchronization of hyperchaotic system via periodically intermittent control

We further study the projective synchronization of a new hyperchaotic system. Different from the most existing methods, intermittent control is applied to chaotic synchronization in the present paper. We formulate the intermittent control system that governs the dynamics of the projective synchronization error, then derive the sufficient conditions for the exponential stability of intermittent control system by using Lyapunov stability theory, and finally establish the periodically intermittent controller according to the stability criterion by which the projective synchronization is expected to be achieved. The analytical results are also demonstrated by several numerical simulations.     

Modified Projective Synchronization of a New Hyperchaotic System via Nonlinear Control

In this paper, a nonlinear control scheme of two identical hyperchaotic Chensystems is developed to realize their modified projective synchronization.We achieve modified projective synchronization between the two identicalhyperchaotic systems by directing the scaling factor onto the desired value. With symbolic computation system Maple and Lyapunov stability theory, numerical simulations are given to perform the process of the synchronization.     

Generalized projective synchronization of two coupled complex networks of different sizes

We investigate a new generalized projective synchronization between two complex dynamical networks of different sizes. To the best of our knowledge, most of the current studies on projective synchronization have dealt with coupled networks of the same size. By generalized projective synchronization, we mean that the states of the nodes in each network can realize complete synchronization, and the states of a pair of nodes from both networks can achieve projective synchronization. Using the stability theory of the dynamical system, several sufficient conditions for guaranteeing the existence of the generalized projective synchronization under feedback control and adaptive control are obtained. As an example, we use Chua's circuits to demonstrate the effectiveness of our proposed approach.     

The impulsive control synchronization of the drive-response complex system

This Letter investigates projective synchronization between the drive system and response complex dynamical system. An impulsive control scheme is adapted to synchronize the drive-response dynamical system to a desired scalar factor. By using the stability theory of the impulsive differential equation, the criteria for the projective synchronization are derived. The feasibility of the impulsive control of the projective synchronization is demonstrated in the drive-response dynamical system.     

Dynamical analysis of a new fractional-order Rabinovich system and its fractional matrix projective synchronization

This paper constructs a new physical system, i.e., the fractional-order Rabinovich system, and investigates its stability, chaotic behaviors, chaotic control and matrix projective synchronization. Firstly, two Lemmas of the new system's stability at three equilibrium points are given and proved. Next, the largest Lyapunov exponent, the corresponding bifurcation diagram and the chaotic behaviors are studied. Then, the linear and nonlinear feedback controllers are designed to realize the system's local asymptotical stability and the global asymptotical stability, respectively. It's particularly significant that, the fractional matrix projective synchronization between two Rabinovich systems is achieved and two kinds of proofs are provided for Theorem 4.1. Especially, under certain degenerative conditions, the fractional matrix projective synchronization can be reduced to the complete synchronization, anti-synchronization, projective synchronization and modified projective synchronization of the fractional-order Rabinovich systems. Finally, all the theoretical analysis is verified by numerical simulation.     

混沌系统的统一投影同步

提出一种实现混沌系统投影同步的统一方法.通过构建一个广义比例矩阵和一个合适的响应系统,建立了混沌投影同步的通用模型,依据比例矩阵的不同种类,可实现广义投影同步、错位投影同步和广义混合错位投影同步等各种类型的混沌投影同步.利用Lyapunov稳定性理论给出了相应的证明,最后以多卷波混沌系统和超混沌Qi系统为例,进行了错位投影同步和广义混合错位投影同步的数值仿真,仿真结果进一步表明了该方法的有效性. 关键词： 混沌系统 广义比例矩阵 统一投影同步     

统一超混沌系统的投影同步

利用两种方法研究了统一超混沌系统的同步问题.首先以全状态混合投影自适应同步方法,基于Lyapunov稳定性理论,设计了自适应控制器,理论证明了该控制器可以实现参数已知的统一超混沌系统的全状态混合映射同步.其次使用主动控制同步方法,设计了同步控制器,实现了统一超混沌系统的完全同步,最后数值仿真实验进一步验证了所提出方案的有效性. 关键词： 统一超混沌系统 自适应控制器 全状态混合投影同步 主动控制同步     

Modified projective synchronization of a fractional-order hyperchaotic system with a single driving variable

In this paper, the modified projective synchronization (MPS) of a fractional-order hyperchaotic system is investigated. We design the response system corresponding to the drive system on the basis of projective synchronization theory, and determine the sufficient condition for the synchronization of the drive system and the response system based on fractional-order stability theory. The MPS of a fractional-order hyperchaotic system is achieved by transmitting a single variable. This scheme reduces the information transmission in order to achieve the synchronization, and extends the applicable scope of MPS. Numerical simulations further demonstrate the feasibility and the effectiveness of the proposed scheme.     

Projective Synchronization Between Two Nonidentical Variable Time Delayed Systems

In this paper,we propose a method for the projective synchronization between two different chaotic systems with variable time delays.Using active control approach,the suitable controller is constructed to make the states of two different diverse time delayed systems asymptotically synchronize up to the desired scaling factor.Based on the Lyapunov stability theory,the sufficient condition for the projective synchronization is calculated theoretically.Numerical simulations of the projective synchronization between Mackey-Glass system and Ikeda system with variable time delays are shown to validate the effectiveness of the proposed algorithm.     

Modified function projective combination synchronization of hyperchaotic systems

In this work, a novel combination synchronization scheme in which synchronization of a new combination hyperchaotic drive system formed by combining state variables of the original drive system with appropriate scaling factors with a response hyperchaotic system is considered. A self-combination system is constructed from hyperchaotic Lorenz system by combining state variables of the Lorenz system with appropriate scaling factors. Modified function projective synchronization between the newly constructed combination hyperchaotic Lorenz system and hyperchaotic Lu system is investigated using adaptive method. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two systems as modified function projective synchronized. Numerical simulations are done to show the validity and effectiveness of the proposed synchronization scheme.     

一种异结构分数阶混沌系统投影同步的新方法

基于Lyapunov稳定性理论和分数阶系统稳定理论以 及分数阶非线性系统性质,提出了一种用来判定分数阶混沌系统是 否稳定的新的判定定理,并把该理论运用于对分数阶混沌系统的控制与 同步,同时给出了数学证明过程,严格保证了该方法的正确性与一般适用性. 运用所提出的稳定性定理,实现了异结构分数阶混沌系统的投影同步. 对分数阶Lorenz混沌系统与分数阶Liu混沌系统实现了投影同步; 针对四维超混沌分数阶系统,也实现了异结构投影同步. 该稳定性定理避 免了求解分数阶平衡点以及Lyapunov指数的问题,从而可以方便地选 择出控制律,并且所得的控制器结构简单、适用范围广. 数值仿真的结果取得了预期的效果,进一步验证了这一稳定性定理的 正确性及普遍适用性.     

参数不确定的分数阶混沌系统广义错位延时投影同步

为进一步增强通信系统中保密通信的安全性,结合广义错位投影同步和延时投影同步,提出了广义错位延时投影同步.以分数阶Chen系统和Lü系统为例,针对两系统参数都不确定,基于分数阶稳定性理论与自适应控制方法,设计了非线性控制器和参数自适应律,实现了广义错位延时同步,并辨识出驱动系统和响应系统中所有不确定参数.理论分析和数值仿真验证了该方法的可行性与有效性.     

基于改进的主动控制法实现混沌系统广义投影同步

通过引进特殊矩阵构造并基于Lyapunov稳定性理论,提出了一种改进的主动控制法来实现混沌系统的广义投影同步.改进后的主动控制不依赖于罗斯-霍维兹判据,与未改进的主动控制相比,简化了相关运算步骤和复杂度.通过对混沌能源系统和Nuclear Spin Generator系统的研究,并与其他同步方法进行比较,说明了该方法具有简单,直观,稳健,高效等优点,且对混沌系统的自结构和异结构广义投影同步均适用.数值模拟的结果进一步表明了该方法的有效性和理论分析的正确性. 关键词： 改进的主动控制 广义投影同步 特殊矩阵构造     

Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems

Scaling factor characterizes the synchronized dynamics of projective synchronization in partially linear chaotic systems but it is difficult to be estimated. To manipulate projective synchronization of chaotic systems in a favored way, a control algorithm is introduced to direct the scaling factor onto a desired value. The control approach is derived from the Lyapunov stability theory. It allows us to arbitrarily amplify or reduce the scale of the response of the slave system via a feedback control on the master system. In numerical experiments, we illustrate the application to the Lorenz system. (c) 2001 American Institute of Physics.     

不同超混沌系统的自适应修正函数投影

研究了具有未知参数的Lorenz-Stenflo(LS)系统和一种新型超混沌系统以及LS系统和超混沌Chen系统的修正函数投影同步问题.利用Lyapunov稳定性理论和主动控制方法,设计自适应控制器和参数更新规则,实现不同超混沌系统的修正函数投影同步,同时估计出系统的未知参数.数值仿真验证了该自适应控制器的有效性.     

On adaptive modified projective synchronization of a supply chain management system

In this paper, the synchronization problem of a chaotic supply chain management system is studied. A novel adaptive modified projective synchronization method is introduced to control the behaviour of the leader supply chain system by a follower chaotic system and to adjust the leader system parameters until the measurable errors of the system parameters converge to zero. The stability evaluation and convergence analysis are carried out by the Lyapanov stability theorem. The proposed synchronization and antisynchronization techniques are studied for identical supply chain chaotic systems. Finally, some numerical simulations are presented to verify the effectiveness of the theoretical discussions.     

基于非线性观测器的一类分数阶混沌系统完全状态投影同步

基于分数阶系统稳定性理论,提出了用状态观测器来实现分数阶混沌系统完全状态投影同步的思想. 设计的状态观测器能够实现一类非线性分数阶系统的完全状态投影同步而不要求分数阶混沌系统是部分线性的,推广了投影同步的应用范围,且无需计算系统的条件Lyapunov指数. 另外,该方法理论严格,设计简单,能够达到任意比例因子的完全状态同步. 最后,利用该方法实现了分数阶Rssler系统的完全状态投影同步,数值仿真结果证实了它的有效性. 关键词： 分数阶 混沌系统 状态观测器 投影同步     

Function projective synchronization in drive-response dynamical network

In this Letter, the function projective synchronization in the drive-response dynamical network is investigated, where the response dynamical network is affected not only by the drive system, but also coupled via a linearly feedback scheme. Based on Lyapunov stability theory, it is shown that the function projective synchronization with desired scaling function can be realized in the drive-response dynamical network by a simple control law. Moreover it is no need for the scaling function to be differentiable, bounded and nonzero all the time. The numerical simulations are provided to verify the theoretical result.     

Lag projective synchronization in fractional-order chaotic (hyperchaotic) systems

In this Letter, a new lag projective synchronization for fractional-order chaotic (hyperchaotic) systems is proposed, which includes complete synchronization, anti-synchronization, lag synchronization, generalized projective synchronization. It is shown that the slave system synchronizes the past state of the driver up to a scaling factor. A suitable controller for achieving the lag projective synchronization is designed based on the stability theory of linear fractional-order systems and the pole placement technique. Two examples are given to illustrate effectiveness of the scheme, in which the lag projective synchronizations between fractional-order chaotic Rössler system and fractional-order chaotic Lü system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved. Corresponding numerical simulations are also given to verify the analytical results.     

Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

We investigate the projective synchronization of different chaotic systems with nonlinearity inputs.Based on the adaptive technique,sliding mode control method and pole assignment technique,a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor.