Chen混沌系统的非线性全局同步控制

研究了Chen提出的一个新的混沌系统的混沌同步问题,利用非线性控制方法设计了三种混沌同步控制器,并用李雅普诺夫方法证明了在混沌控制器作用下,驱动、响应混沌系统可以实现全局同步.数值仿真结果表明,所设计的三种混沌控制器都能有效的实现混沌同步,并且具有很强的鲁棒性.     

异结构离散型混沌系统的延迟同步

以异结构离散型混沌系统为研究对象,设计了一种延迟同步控制器实现了离散型Henon混沌系统和Ikeda混沌系统之间的同步控制．根据稳定性定理,确定了延迟同步控制器的结构以及系统状态变量之间的误差方程．设计的延迟同步控制器对于不同的离散型混沌系统具有统一的形式,可以实现任意异结构离散型混沌系统之间的延迟同步．数值仿真模拟进一步验证了该控制器的有效性．     

多涡旋混沌同步和分数阶混沌同步

为探讨混沌同步现象和相应的动力学特性,研究了两类特殊的混沌系统即多涡旋混沌系统和分数阶混沌系统的同步.为此,设计了一种非线性反馈控制器,实现了多涡旋类Lorenz的混沌吸引子的投影同步;通过改变投影同步的比例系数,获得了与激励系统相对应的状态变量的任意比例输出.此设计还实现了分数阶超混沌系统的状态向量与任意信号的追踪同步,从而控制分数阶混沌信号趋于期望的周期轨道或平衡点,并实现分数阶混沌系统与整数阶混沌系统的异构追踪同步.最后设计了具有分数阶混沌特性的电路,借助仿真实验证实了分数阶超混沌系统的动力学行为.这些研究结果可以应用于许多领域,例如宏观经济系统的数据分析、保密通讯系统分析与设计等.     

分数阶双指数混沌系统的自适应滑模同步

研究了分数阶双指数混沌系统的自适应滑模同步问题.通过设计滑模函数和控制器,构造了平方Lyapunov函数进行稳定性分析.利用Barbalat引理证明了同步误差渐近趋于零,获得了系统取得自适应滑模同步的充分条件.数值仿真结果表明:选取适当的控制器及与滑模函数,分数阶双指数混沌系统取得自适应滑模同步.     

一类不确定混沌系统的自适应同步

讨论了混沌系统的同步问题 .对一类不确定混沌系统 ,提出了一个新的自适应同步方法 ,可使响应系统在自适应控制器的控制下 ,实现与不确定混沌系统的同步 .最后给出了一个设计实例 .     

基于主动滑模控制的混沌系统函数投影同步

研究了一类混沌系统的函数投影同步问题.基于Lyapunov稳定性理论和主动滑模控制方法,设计了主动滑模控制器,实现混沌系统的函数投影同步.数值仿真验证了该控制器的有效性和正确性.     

受扰不确定混沌系统的降阶修正函数投影同步

研究了具有不同阶数的受扰不确定混沌系统的降阶修正函数投影同步问题.基于Lyapunov稳定性理论和自适应控制方法,设计了统一的非线性状态反馈控制器和参数更新规则,使得混沌响应系统按照相应的函数尺度因子矩阵和混沌驱动系统的部分状态变量实现同步.方法考虑了实际系统中的模型不确定性和外界扰动,具有较强的实用性和鲁棒性.数值仿真证明了控制方法的有效性.     

一个四翼混沌系统的广义控制与同步

针对四翼混沌系统的控制和同步问题,采用反馈控制方法将系统的混沌运动控制到稳定态;根据Routh-Huriwtz准则获得了系统达到控制目标时反馈系数所满足的条件,通过设计控制器研究系统的广义控制与同步.在此基础上给出了响应系统同时含有控制变量时,系统的广义混合控制与同步运动行为,并从理论分析和Maple数值仿真验证了同步方法的可行性.     

新的分数阶混沌系统及其同步

提出一个新的分数阶混沌系统,该系统含有三个参数,三个非线性项.通过理论分析,给出了分数阶混沌系统存在混沌吸引子的必要条件,通过数值仿真给出了混沌吸引子的图像,接着设计自适应同步控制器和参数自适应律,实现分数阶混沌系统的同步,数值仿真的结果表明设计控制器很好的实现了驱动系统和响应系统的同步.     

基于线性控制的分数阶混沌系统的对偶投影同步

分数阶混沌系统的对偶同步是一个新的同步方法.有关分数阶混沌系统对偶投影同步的研究较少.基于分数阶系统的稳定性理论,通过设计线性控制器研究了分数阶混沌系统的对偶投影同步.给出了一个实现分数阶混沌系统对偶投影同步的一般方法,推广了现有对偶同步的研究结果,通过分数阶Van der Pol系统和分数阶Willis系统的数值仿真证实了该方法的有效性.     

Dynamical analysis and numerical simulation of bloch chaotic system

In this article, some dynamics of Bloch chaotic system have been studied. Based on Lagrange multiplier method, optimization theory, and the generalized positively definite and radially unbound Lyapunov functions with respect to the parameters of the system, we derive the ultimate bound and a family of mathematical expressions of globally exponentially attractive sets for this system with respect to the parameters of system. The results obtained in this article provides theory basis for chaotic synchronization, chaotic control, Hausdorff dimension, and Lyapunov dimension of chaotic attractors of Bloch chaotic system. © 2016 Wiley Periodicals, Inc. Complexity 21: 201–206, 2016     

Qualitative behavior of the Lorenz‐like chaotic system describing the flow between two concentric rotating spheres

In this article, the bounds of the Lorenz‐like chaotic system describing the flow between two concentric rotating spheres have been studied. Based on Lagrange multiplier method, the function extremum theory and the generalized positive definite and radially unbound Lyapunov functions with respect to the parameters of the system, we derive the ultimate bound and the globally exponentially attractive set for this system. The results that obtained in this article provides theory basis for chaotic synchronization, chaotic control, Hausdorff dimension and the Lyapunov dimension of chaotic attractors. © 2016 Wiley Periodicals, Inc. Complexity 21: 67–72, 2016     

Adaptive projective synchronization for a class of switched chaotic systems

This paper addresses the problem of projective synchronization of chaotic systems and switched chaotic systems by adaptive control methods. First, a necessary and sufficient condition is proposed to show how many state variables can realize projective synchronization under a linear feedback controller for the chaotic systems. Then, accordingly, a new algorithm is given to select all state variables that can realize projective synchronization. Furthermore, according to the results of the projective synchronization of chaotic systems, the problem of projective synchronization of the switched chaotic systems comprised by the unified chaotic systems is investigated, and an adaptive global linear feedback controller with only one input channel is designed, which can realize the projective synchronization under the arbitrary switching law. It is worth mentioning that the proposed method can also realize complete synchronization of the switched chaotic systems. Finally, the numerical simulation results verify the correctness and effectiveness of the proposed method.     

Design of $n$-dimensional multi-scroll Jerk chaotic system and its performances

Based on three-order Jerk and high-order Jerk chaotic systems, a general approach is proposed to generate $n$-dimensional multi-scroll Jerk chaotic attractors via nonlinear control. Dynamics of the $n$-dimensional multi-scroll Jerk chaotic systems are analyzed by means of the largest Lyapunov exponent and multi-scale permutation entropy complexity. As an experimental verification, four-dimensional Jerk chaotic attractors are implemented by analog circuits. Results of the numerical simulation are consistent with that of the hardware experiments. It shows that the method of obtaining complex Jerk chaotic attractors is effective.     

Counteracting the dynamical degradation of digital chaos via hybrid control

Chaotic systems would degrade owing to finite computing precisions, and such degradation often seriously affects the performance of digital chaos-based applications. In this paper, a chaotification method is proposed to solve the dynamical degradation of digital chaotic systems based on a hybrid structure, where a continuous chaotic system is applied to control the digital chaotic system, and a unidirectional coupling controller that combines a linear external state control with a modular function is designed. Moreover, we proof rigorously that a class of digital chaotic systems can be driven to be chaotic in the sense that the system is sensitive to initial conditions. Different from the existing remedies, this method can recover the dynamical properties of system, and even make some properties better than those of the original chaotic system. Thus, this new approach can be applied to the fields of chaotic cryptography and secure communication.     

A new 4-D non-equilibrium fractional-order chaotic system and its circuit implementation

A new 4-D fractional-order chaotic system without equilibrium point is proposed in this paper. There is no chaotic behavior for its corresponding integer-order system. By computer simulations, we find complex dynamical behaviors in this system, and obtain that the lowest order for exhibiting a chaotic attractor is 3.2. We also design an electronic circuit to realize this 4-D fractional-order chaotic system and present some experiment results.     

动力系统实测数据的非线性混沌模型重构

动力系统实测非线性混沌数据的模型重构技术是相空间重构的重要内容。在判定了实测数据的非线性混沌特征,计算了实测数据的分维数,Lyapunov指数,并对其进行了本征值分解和噪声去除及确定其模型阶数以后,提出了一个动力系统实测数据的非线性混沌模型,给出了相应的模型参数辨识方法,并用其确立的混沌模型进行了预测工作,计算结果表明:模型参数辨识方法能迅速地将参数估计值带到多峰目标函数的全局最少值附近,然后再采用优化理论能较准确地求出模型的参数,用得到的混沌模型对系统进行预测工作其预测效果良好,且混沌时序不可能作长期预测。     

Function vector synchronization based on fuzzy control for uncertain chaotic systems with dead‐zone nonlinearities

In this article, a fuzzy adaptive control scheme is designed to achieve a function vector synchronization behavior between two identical or different chaotic (or hyperchaotic) systems in the presence of unknown dynamic disturbances and input nonlinearities (dead‐zone and sector nonlinearities). This proposed synchronization scheme can be considered as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization, generalized projective synchronization, and so forth) in the sense that the master and slave outputs are assumed to be some general function vectors. To practically deal with the input nonlinearities, the adaptive fuzzy control system is designed in a variable‐structure framework. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is used to prove the boundedness of all signals of the closed‐loop control system as well as the exponential convergence of the corresponding synchronization errors to an adjustable region. The synchronization between two identical systems (chaotic satellite systems) and two different systems (chaotic Chen and Lü systems) are taken as two illustrative examples to show the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 234–249, 2016     

The control of chaotic systems with unknown parameters and external disturbance via backstepping‐like scheme

This article addresses the adaptive control of chaotic systems with unknown parameters, model uncertainties, and external disturbance. We first investigate the control of a class of chaotic systems and then discuss the control of general chaotic systems. Based on the backstepping‐like procedure, some novel criteria are proposed via adaptive control scheme. As an example to illustrate the application of the proposed method, the control and synchronization of the modified Chua's chaotic system is also investigated via a single input. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed approach. © 2016 Wiley Periodicals, Inc. Complexity 21: 573–583, 2016