统一混沌系统的控制

对统一混沌系统建立了自反馈控制、错位反馈控制和自适应控制方法，在理论上给予严格证明，数值仿真表明这些方法是很有效的.还纠正了文献［１０］的某些不足. 关键词： 统一混沌系统 反馈 自适应 控制 Routh-Hurwitz定理     

外力驱动的混沌摆实验仪在研究混沌效用上的应用

依据非线性动力学混沌理论,采用受外力驱动的转动马达装置,依托PASCO系统的数据采集软件,开发了适应大学物理实验的受外力驱动的混沌摆实验。探讨了新型基于外力驱动的混沌摆实验仪在研究混沌效用上的应用,实验发现利用该装置可以直观的研究系统的初值敏感性,奇异子现象等,操作简单、直观、灵敏度高,实验除了具有实际应用价值外,同时适合在高等学校大学物理基础实验中开设出相应的实验教学内容。     

单模激光Lorenz系统与3D混沌系统之间的混沌同步

研究了异结构混沌系统之间的同步控制问题.采用非线性反馈控制方法实现了3D混沌系统和单模激光Lorenz混沌系统之间的混沌同步.根据系统的稳定性理论,得到了非线性反馈控制器的结构和反馈控制增益的取值范围.仿真模拟的结果表明:目标系统和响应系统达到完全同步,两系统状态变量随时间的演化轨迹完全一致,并且误差变量经过短暂的时间序列以后始终平稳地趋于零.仿真模拟的结果证明了这种方法的有效性.     

A New Approach for Controlling Chaos Based on Direct Optimizing Predictive Control

We introduce the predictive control theory into the study of chaos control and propose a direct optimizing predictive control algorithm based on a neural network model. The proposed control system stabilizes the chaotic motion in an unknown chaotic system onto the desired target trajectory. Compared with the existing similar algorithms, the proposed control system has faster response, so it requires much shorter time for the stabilization of the chaotic systems.The proposed approach can control hyperchaos and the algorithm is simple. The convergence of the control algorithm and the stability of the control system can be guaranteed. The theoretic analysis and simulations demonstrate the effectiveness of the algorithm.     

一类四维混沌系统切换混沌同步

构建了一类可切换的四维混沌系统，通过选择器实现这类系统间的随机切换.简要地分析了四维混沌系统平衡点的性质、混沌吸引子的相图和Lyapunov指数等特性，并设计了实现四维混沌系统切换的实际电路.利用非线性反馈控制方法实现了这类系统与其中某个系统之间的切换混沌同步.根据系统稳定性理论，得到了非线性反馈控制器的结构和系统达到混沌同步时反馈控制增益的取值范围. 关键词： 非线性反馈 混沌同步 四维混沌系统     

声光双稳系统混沌的控制

对声光双稳系统的混沌态提出参数连续延时反馈的控制技术。数值分析表明，在一定的控制强度下，这种控制使系统在原混沌区具有负的最大李亚普诺夫指数，并且能够保证控制的目标状态是原系统的失稳不动点中稳定周期轨道。文章通过与实验结果的比较，验证了本控制方法的有效性。     

平移法控制离散系统的倍周期分岔和混沌

利用平移系统的方法,实现了对离散非线性动力学系统的倍周期分岔的控制和混沌吸引子不稳定周期轨道的控制.只要选择适当的平移参数,使系统平移到不同位置,就可将系统控制在不同的预期轨道.将此方法应用到Logistic映射和Henon映射中取得了很好的控制效果.     

基于重复混沌扩频序列的差分混沌键控系统

提出一种基于可重复混沌扩频序列的差分混沌键控保密通信系统, 并对该系统的误码率进行分析。通过复制差分混沌键控调制信号的参考信号产生重复的混沌扩频序列, 再和经串并转换后的部分数据流相乘, 其余并行数据流按照传统差分混沌键控进行调制, 两部分信号相加后发送到信道中进行传输。在接收端进行相关解调恢复出原信息。理论分析和仿真结果表明: 在多径衰落信道下, 该系统的误码率低于DCSK、CDSK和CD-DCSK系统, 且扩频因子越小, 误码率越低。信道中叠加服从高斯分布噪声时的系统误码率相比叠加服从瑞利分布噪声时的小。     

基于PASCO系统的混沌摆实验

基于PASCO系统研制了受周期外力驱动的混沌摆实验仪,调节混沌摆系统的参量可演示非线性动力学特征行为,描绘了无驱动及有驱动下的系统相位图,并分析了初值敏感性、奇异性(奇异吸引子)现象.应用混沌摆的动力学方程,进行Matlab仿真实验.实验结果表明:混沌摆实验系统动力学的性质依赖于振动频率值,系统驱动振幅必须大于一定阈值是混沌相出现的必要条件.     

一类新混沌系统的线性状态反馈控制

研究了一类新混沌系统的控制问题.利用Routh-Hurwitz准则对受控系统进行了稳定性分析，结合线性状态反馈方法理论上严格证明了达到控制目标反馈系数的选择原则.数值研究证明了该方法能够有效地控制混沌系统到失稳的平衡点或周期解，同时控制效果在弱噪声干扰下具有很强的鲁棒性. 关键词： 新混沌系统 线性状态反馈控制 Routh-Hurwitz准则 噪声     

Chaos control and reduced-order generalized synchronization for the Chen——Liao system

This paper deals with the problem of chaos control and synchronization of the Chen--Liao system. From rigorous mathematic justification, the chaotic trajectories of the Chen--Liao system are led to a type of points whose four-dimensional coordinates have a particular functional relation among them. Meanwhile, a new synchronization manner, reduced-order generalized synchronization (RGS), is proposed which has the characteristic of having a functional relation between the slave and the partial master systems. It is shown that this new synchronization phenomenon can be realized by a novel technique. Numerical simulations have verified the effectiveness of the proposed scheme.     

电光双稳系统中混沌控制的动态存储

报道了电光双稳系统输出振荡混沌区的二次反分岔区域中使用连续自反馈控制的方法实现动态存储的实验研究。李雅普诺夫指数分析和计算机数值模拟表明这处方法是可行的，混沌控制前后输出振荡分岔图的对比显示了使用这种方法实现稳定动态存储的物理机制。实验结果与理论模拟一致，动态存储，电光双稳系统。     

耦合双稳映象格子模型的时空混沌控制

变量反馈技术实现了耦合双稳映象格子模型的时空混沌控制.数值实验结果表明,利用不同的反馈技术和不同的反馈强度,可以将双稳映象系统的混沌及耦合双稳映象格子模型的时空混沌控制到不动点或周期轨道.变量反馈控制法除了局域双稳映象系统的定态点外,不需要先获取耦合双稳映象格子时空系统的动力学信息,它对抑制耦合双稳映象系统中的湍流具有一定的指导作用.     

Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System

In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed four-dimensional (4D) Euler equation. The generalized Hamiltonian energy function has been given, and it is composed of conservative and non-conservative parts of the Hamiltonian. The Hamiltonian of the Euler equation remains constant, while the three-terminal memristor’s Hamiltonian is mutative, causing non-conservation in energy. Through proof, only centers or saddles equilibria exist, which meets the definition of the conservative system. A non-Hamiltonian conservative chaotic system is proposed. The Hamiltonian of the conservative part determines whether the system can produce chaos or not. The non-conservative part affects the dynamic of the system based on the conservative part. The chaotic and quasiperiodic orbits are generated when the system has different Hamiltonian levels. Lyapunov exponent (LE), Poincaré map, bifurcation and Hamiltonian diagrams are used to analyze the dynamical behavior of the non-Hamiltonian conservative chaotic system. The frequency and initial values of the system have an extensive variable range. Through the mechanism adjustment, instead of trial-and-error, the maximum LE of the system can even reach an incredible value of 963. An analog circuit is implemented to verify the existence of the non-Hamiltonian conservative chaotic system, which overcomes the challenge that a little bias will lead to the disappearance of conservative chaos.     

分数阶电子振荡器的混沌及其控制

本文研究了分数阶混沌电子振荡器的混沌行为。研究表明：混沌存在于阶数低于3阶的分数阶电子振荡器中，为了说明混沌行为的连续性，本文对分数阶电子振荡器进行了降阶、升阶 （2.8—3.2阶）的仿真分析。最后，本文基于自适应Backstepping法研究了分数阶电子振荡器的混沌控制，仿真结果表明了该方法的有效性和可行性。     

Image Security Based on Three-Dimensional Chaotic System and Random Dynamic Selection

Image encryption based on a chaos system can effectively protect the privacy of digital images. It is said that a 3D chaotic system has a larger parameter range, better unpredictability and more complex behavior compared to low-dimension chaotic systems. Motivated by this fact, we propose a new image cryptosystem that makes use of a 3D chaotic system. There are three main steps in our scheme. In the first step, the chaotic system uses the hash value of the plaintext image to generate three sequences. In step two, one of the sequences is used to dynamically select confusion and diffusion methods, where confusion and diffusion have three algorithms, respectively, and will produce 3²ⁿ (n > 100) combinations for encryption. In step three, the image is divided into hundreds of overlapping subblocks, along with the other two sequences, and each block is encrypted in the confusion and diffusion process. Information entropy, NPCR, UACI results and various security analysis results show that the algorithm has a better security performance than existing, similar algorithms, and can better resist clipping, noise, statistical analysis and other attacks.     

FPGA-Based Implementation and Synchronization Design of a New Five-Dimensional Hyperchaotic System

Considering the security of a communication system, designing a high-dimensional complex chaotic system suitable for chaotic synchronization has become a key problem in chaotic secure communication. In this paper, a new 5-D hyperchaotic system with high order nonlinear terms was constructed and proved to be hyperchaotic by dynamical characterization characteristics, the maximum Lyapunov exponent was close to 2, and there was a better permutation entropy index, while a valid chaotic sequence could be generated in three cycles in the FPGA (Field Programmable Gate Array)-based implementation. A multivariable nonlinear feedback synchronous controller based on FPGA was proposed to design and implement synchronization of high order complex hyperchaotic systems. The results show that the error signal converged to 0 rapidly under the effect of the nonlinear feedback synchronous controller. This lays the foundation for the synchronization of high order complex chaotic systems.     

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems.Based on Lyapunov stability theory and numerical differentiation,a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems.Numerical simulation results are presented to illustrate the effectiveness of this method.     

变形耦合发电机系统中的混沌控制

分别利用反馈和非反馈方法研究了变形耦合发电机系统的混沌控制问题，并基于Lyapunov直接法和Routh-Hurwitz判据讨论了受控变形耦合发电机系统的混沌轨道达到不稳定平衡点或极限环时的条件，同时给出了理论上的证明.数值模拟进一步验证了这两种方法的有效性. 关键词： 变形耦合发电机系统 反馈法 非反馈法 混沌控制     

Controlling Chaos of a Delayed Optical Bistable System

High-dimensional chaos was controlled with the occasional proportional feedback technique in a delayed optical bistable system which consists of a laser diode interferometer with a delayed opto-electronic feedback loop. Both the experiment and the numerical simulation showed that a large number of periodic orbits can be stabilized by controlling the chaotic attractor. The transient state of the trajectory under control was demonstrated.