Modified scaling function projective synchronization of chaotic systems

This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point, a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle's invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.     

部分线性的分数阶混沌系统修正函数投影同步

针对一类部分线性的分数阶混沌系统修正函数投影同步问题, 可通过单变量耦合构造出这类系统的响应系统, 从而提出修正函数投影同步的设计方法. 根据Routh-Hurwitz条件, 给出耦合部分线性系统实现修正函数投影同步的方法, 并设计了控制器. 该方法中控制器和误差动态方程的选择都是确定的, 理论分析和数值仿真都说明了该方法在部分线性的分数阶混沌系统中应用具有可行性和有效性. 关键词： 分数阶混沌系统 部分线性 修正函数投影同步     

一类混沌系统的修正函数投影同步

针对一类混沌系统,通过构造合适的响应系统,提出一种修正函数投影同步方法.基于单向耦合同步原理,给出了两种响应系统的设计方案,由于只需向响应系统传送一个驱动变量即可实现混沌修正函数投影同步,因而实用性更强.利用Lyapunov稳定性理论给出了相应的证明. 最后以一个超混沌系统进行了数值仿真,仿真结果进一步表明该方法的有效性. 关键词： 混沌系统 修正函数投影同步 单向耦合     

Adaptive function projective synchronization of uncertain complex dynamical networks with disturbance

We investigate the problem of function projective synchronization (FPS) in drive-response dynamical networks with non-identical nodes. An adaptive controller is proposed for the FPS of complex dynamical networks with uncertain parameters and disturbance. Not only are the unknown parameters of the networks estimated by the adaptive laws obtained from the Lyapunov stability theory and Taylor expansions, but the unknown bounded disturbances are also simultaneously conquered by the proposed control. Finally, a numerical simulation is provided to illustrate the feasibility and effectiveness of the obtained result.     

Adaptive projective synchronization with different scaling factors in networks

We study projective synchronization with different scaling factors （PSDF） in N coupled chaotic systems networks. By using the adaptive linear control, some sufficient criteria for the PSDF in symmetrical and asymmetrical coupled networks are separately given based on the Lyapunov function method and the left eigenvalue theory. Numerical simulations for a generalized chaotic unified system are illustrated to verify the theoretical results.     

带未知扰动的多涡卷混沌系统修正函数时滞投影同步

研究了带有未知外部扰动的不同多涡卷混沌系统修正函数时滞投影同步问题. 基于Lyapunov稳定性理论, 采用模糊自适应控制的方法设计自适应同步控制器及参数的更新规则. 该控制器在实现混沌系统修正函数时滞投影同步的同时对外界扰动的变化能保持较好的稳定性. 数值仿真的结果进一步验证了该方法的有效性.     

含有不确定项的混沌系统自适应修正函数投影同步

针对一类含有不确定项的混沌系统修正函数投影同步问题, 提出了自适应修正函数投影同步方法.根据Lyapunov稳定性理论, 给出了两种响应系统的设计方案,并设计了控制器和自适应律. 研究表明,所设计的控制策略对外界干扰有较强的鲁棒性, 且不需要事先已知不确定项的上界,通过引入加速因子,可任意配置同步响应速度, 具有较高的使用价值.理论分析及仿真结果验证了该方法的有效性.     

两个四维混沌系统广义投影同步

利用主动控制同步法设计合适的非线性反馈控制器，实现两个相同的四维混沌系统的同结构广义投影同步，以及实现两个不同的新型四维混沌系统异结构广义投影同步.通过改变广义投影同步的比例因子，获得任意比例于原驱动混沌系统输出的混沌信号.数值仿真表明了所设计的控制器有效性和理论推导的正确性.     

复杂Dynamos混沌系统的追踪控制与同步

基于系统稳定性理论,设计合适的新型非线性反馈控制器,实现复杂Dynamos混沌系统的状态向量与任意给定的不同参考信号追踪广义投影同步.以追踪控制超混沌系统、混沌系统、正弦余弦信号以及不动点为例,通过改变比例因子,可以获得多个不同混沌系统之间的异结构广义投影同步以及与正弦波形的广义同步,或者将复杂Dynamos混沌系统控制到期望的平衡点.数值仿真进一步表明了该方法的有效性. 关键词： 复杂Dynamos混沌系统 追踪控制 广义投影同步 平衡点     

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.     

Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance

Based on fractional-order Lyapunov stability theory, this paper provides a novel method to achieve robust modified projective synchronization of two uncertain fractional-order chaotic systems with external disturbance. Simulation of the fractional-order Lorenz chaotic system and fractional-order Chen＇s chaotic system with both parameters uncertainty and external disturbance show the applicability and the efficiency of the proposed scheme.     

Cluster projective synchronization of complex networks with nonidentical dynamical nodes

We investigate a new cluster projective synchronization(CPS) scheme in time-varying delay coupled complex dynamical networks with nonidentical nodes.Based on the community structure of the networks,the controllers are designed differently for the nodes in one community,which have direct connections to the nodes in the other communities and the nodes without direct connections to the nodes in the other communities.Some sufficient criteria are derived to ensure the nodes in the same group projectively synchronize and there is also projective synchronization between nodes in different groups.Particularly,the weight configuration matrix is not assumed to be symmetric or irreducible.The numerical simulations are performed to verify the effectiveness of the theoretical results.     

Arbitrary full-state hybrid projective synchronization for chaotic discrete-time systems via a scalar signal

In this paper we present a new projective synchronization scheme,where two chaotic(hyperchaotic) discretetime systems synchronize for any arbitrary scaling matrix.Specifically,each drive system state synchronizes with a linear combination of response system states.The proposed observer-based approach presents some useful features:i) it enables exact synchronization to be achieved in finite time(i.e.,dead-beat synchronization);ii) it exploits a scalar synchronizing signal;iii) it can be applied to a wide class of discrete-time chaotic(hyperchaotic) systems;iv) it includes,as a particular case,most of the synchronization types defined so far.An example is reported,which shows in detail that exact synchronization is effectively achieved in finite time,using a scalar synchronizing signal only,for any arbitrary scaling matrix.     

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.     

Function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems

This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional (3D) integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.     

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.     

Adaptive generalized projective synchronization in different chaotic systems based on parameter identification

In this Letter, the generalized projective synchronization of different chaotic systems with unknown parameters is investigated. By Lyapunov stability theory, the adaptive control method is proposed to achieve above synchronization phenomenon. Meanwhile, according to the invariance principle of differential equations, unknown parameter can be estimated accurately. The schemes are successfully applied to two groups of examples: the anti-phase synchronization between Lorenz system and Chen system; the complete synchronization between hyper-chaotic system and generalized Loren system. The corresponding numerical results are presented to verify the effectiveness of this method.     

Adaptive generalized projective synchronization of two different chaotic systems with unknown parameters

This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov stability theory, and employs a combination of feedback control and adaptive control. With this method one can achieve the generalized projective synchronization and realize the parameter identifications between almost all chaotic （hyperchaotic） systems with unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.     

Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application

Multi-link networks are universal in the real world such as relationship networks, transportation networks, and communication networks. It is significant to investigate the synchronization of the network with multi-link. In this paper, considering the complex network with uncertain parameters, new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization (FTCPS). In addition, based on fractional-order Lyapunov functional method and finite-time stability theory, the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters. Meanwhile, numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters. Finally, the network is applied to image encryption, and the security analysis is carried out to verify the correctness of this method.