异结构超混沌系统动力学分析和同步控制策略研究

基于混沌同步控制理论研究,结合同步控制与线性反馈控制方法,提出一种针对异结构超混沌系统的同步控制策略.在Chua混沌系统和Chen混沌系统理论研究基础上,通过增加两个反馈控制器得到两个异结构五阶混沌系统,对其进行动力学分析,证实其为五阶超混沌系统,并基于Mathmatic环境下对其模型进行数值仿真,得到其平面相图.采用全状态投影同步方法实现对其同步控制,并用龙格库塔算法进行数值模拟,证实该同步方法有效可行.     

非恒同混沌系统的全状态广义同步

在已有的广义同步定义基础上,提出了一种新的概念-非恒同混沌系统的全状态广义同步(FSGS),给出了实现全状态广义同步的统一的控制器形式,该控制器适用范围人,结构相对简单,并且是白适应的.以Chua电路、Lorenz系统、Rossler系统和Liu系统为例,数值实验验证了该方法的有效性,该控制方法可以很快的实现两个混沌系统的全状态广义同步.     

异构超混沌广义同步系统构造及其电路仿真

在三维新混沌Chen系统基础上构建了一个四维超混沌系统。根据Lyapunov稳定性原理,采用自适应控制方法,在新构建的四维超混沌系统和四维超混沌Chen系统之间设计广义同步控制器,对控制器中的变量参数估计值和外部参数值进行广义同步实现的可行性进行讨论,进而将异构系统的广义同步问题转换为对控制器的选择。通过对不同参数估计值的比较分析得出合适的取值,达到了良好的广义同步效果。最后设计了一种实现广义混沌同步的基本电路原理图,数值仿真和电路实验结果表明了该方法的有效性,以及电路的可行性和实用性。     

忆阻混沌系统的有限时间控制

忆阻器作为电路中的第四个基本元件,于1971年由蔡教授提出。忆阻器是非线性的,具有很多特殊的属性。目前,基于忆阻器的电路设计成为研究热点,基于忆阻器的混沌系统也吸引了很多学者的关注。基于有限时间稳定的思想,研究了一类五阶忆阻混沌系统的全局稳定性及有限时间镇定问题,设计了非连续的状态反馈控制器,使得忆阻混沌系统全局指数稳定。仿真实验结果验证了该方法的正确性和有效性。     

Anti‐Synchronization and Intermittent Anti‐Synchronization of Two Identical Delay Hyperchaotic Chua Systems Via Linear Control

This work is concerned with anti‐synchronization and intermittent anti‐synchronization of two identical delay hyperchaotic Chua systems with linear control approaches. In the first two schemes, based on Lyapunov stability theory, some sufficient conditions for achieving anti‐synchronization of two identical delay hyperchaotic Chua systems are derived, numerical simulation results are presented to demonstrate the effectiveness of the proposed anti‐synchronization schemes. In the third scheme, the anti‐synchronization conditions are obtained by numerical method. In the fourth scheme, only one state of the response system is controlled via linear control, we report an interesting phenomenon of intermittent anti‐synchronization.     

连续混沌系统的稳定性分析

在用穷尽熵计算混沌序列类随机性强弱的基础上,提出了k错穷尽熵的定义,并证明了它的两个基本性质,然后用此方法分析了三种常见连续混沌系统Lorenz系统、Rossler系统、Chua’s系统的类随机性的稳定性。仿真结果表明此方法能反映连续混沌系统的随机本质;作为随机源,Chua’s系统比Lorenz系统和R?ssler系统更好。     

超混沌系统的构造方法研究

分析了Lorenz系统的结构,提出了基于Lorenz系统通过增加微分方程组维数和引入非线性项来构造超混沌系统要满足的必要条件和规则,并按照引入新变量增加微分方程组维数和增加非线性项的构造超混沌系统规则,分别构造了一个新的四维超混沌Lorenz系统和一个五维超混沌Lorenz系统,最后将所提出的两个新的超混沌Lorenz系统与其他混沌系统进行了对比分析,结果表明新的混沌系统具有良好的动力学特性,可提供更大的密钥空间,以及增强了动力学系统的非线性,为图像加密提供了新方法,同时也丰富了混沌学理论。     

蔡氏混沌电路频谱分布与元件参数的选择

以蔡氏电路为研究对象,依据电路方程从理论上给出了在保持混沌特性不变时的三种改变电路元件参数的途径,并进行了Multisim仿真实验.比较不同情况下混沌系统各电路变量的频谱分布曲线,发现在一定参数空间内仿真实验的结果和理论分析一致.这将为设计不同频率需求的混沌电路提供很好的设计思路,也可以在一定范围内选择不同电路元件参数,来改善所需混沌系统的频率特性,设计出更符合需求的混沌电路.     

Hybrid state-space fuzzy model-based controller with dual-ratesampling for digital control of chaotic systems

We develop a hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems. A Takagi-Sugeno (TS) fuzzy model is used to model the chaotic dynamic system and the extended parallel-distributed compensation technique is proposed and formulated for designing the fuzzy model-based controller under stability conditions. The optimal regional-pole assignment technique is also adopted in the design of the local feedback controllers for the multiple TS linear state-space models. The proposed design procedure is as follows: an equivalent fast-rate discrete-time state-space model of the continuous-time system is first constructed by using fuzzy inference systems. To obtain the continuous-time optimal state-feedback gains, the constructed discrete-time fuzzy system is then converted into a continuous-time system. The developed optimal continuous-time control law is finally converted into an equivalent slow-rate digital control law using the proposed intelligent digital redesign method. The main contribution of the paper is the development of a systematic and effective framework for fuzzy model-based controller design with dual-rate sampling for digital control of complex such as chaotic systems. The effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic Chua circuit     

时变时滞非线性系统的间歇控制

时变时滞广泛存在于各种非线性系统中,研究了时变时滞非线性系统的间歇控制及其在保密通信中的应用问题,提出了一种间歇控制策略,理论上分析了其正确性,并且给出一个定理来确定控制器的相关参数。根据提出的定理,设计出间歇控制器使得两个含有时变时滞的Chua电路指数达到同步。将该方法应用到混沌保密通信中,在两个系统达到同步的基础上,发送端的信号能够在接收端很好地恢复出来,表明了该方法的可行性。     

新超混沌系统的动力学行为及自适应控制和同步

分析了一个新混沌系统的超混沌动力学行为,给出了这个未知参数的超混沌系统的自适应控制和同步问题的数值模拟结果.运用相图、分岔图、Lyapunov指数谱和庞加莱截面图,返回映射和功率谱等揭示了系统混沌行为的普适特征,基于Lyapunov稳定性理论,采用自适应控制方法将系统的混沌运动控制到一个不稳定的平衡点.此外,设计自适应控制律以实现超混沌系统的状态同步,仿真结果表明所提出的方法的有效性.     

一类分数阶超混沌系统的同步及其应用

应用分数阶微积分稳定性理论,提出了一类分数阶超混沌系统同步控制的新方法,通过在分数阶超混沌响应系统中设计两个控制器,实现了分数阶超混沌Chen系统之间的同步。并将该方案应用到保密通信中,利用混沌掩盖技术,实现了复杂非周期信号的安全传送,在接收端通过去掩盖,毫无失真地恢复了有用传送信号。数值仿真和理论分析结果的一致性表明了该方案的有效性和可行性。     

基于云计算的混合超混沌加密算法研究

针对云计算环境中的数据安全问题,提出了一种基于云计算的混合超混沌加密算法。首先,选取三个超混沌系统的初始值作为密钥参数,利用超混沌系统更加复杂的动力学行为产生随机特性良好的混沌序列;接着,对三个超混沌系统进行预处理后,进而设计一个混合超混沌分组加密方案;最后,基于MapReduce的云计算分布式编程模型,设计并行超混沌加密算法。实验结果和分析表明,算法具有执行效率高,密钥空间大及密钥敏感性良好的特性。     

Modelling and simulation of the multi-scroll chaotic attractors using bond graph technique

This paper presents modelling and simulation of multi-scroll chaotic attractors by using a new simple and more general bond graph model. For this purpose, the multi-segment non-linear resistor in Chua’s circuit is modelled by using piecewise linearization with control inequalities. The proposed model consists of active/passive circuit elements, voltage-controlled current source (VCCS) and ideal switches. The advantage of modelling multi-segment non-linear resistor by using control inequalities yields minimum number of the switches and sources. Proposed model is simple and more general and, especially, could be used in various kinds of non-linear circuit in the chaos studies. Generally, two different non-linear resistor models are used in the literature to obtain odd and even numbers of the scrolls. In this study, one model is developed for both multi-scroll chaotic attractors. In this paper, bond graph simulation of Chua’s circuit is realized by using proposed model. The BONDAS program that developed in Matlab is used for the simulations, and satisfactory results are obtained.     

Exponential synchronization of two totally different chaotic systems based on a unified model

This paper presents an exponential synchronization scheme between two chaotic systems with different structures and parameters. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these totally different chaotic systems. A novel state feedback control law is established to exponentially synchronize the two unified models with different parameters. Most chaotic systems with different structures and parameters, such as Hopfield neural networks, cellular neural networks, Chua’s circuits, unified chaotic systems, Qi systems, and chaotic recurrent multilayer perceptrons, can be transformed into this unified model with the synchronization controller designed in a unified way. Two numerical examples are exploited to illustrate the effectiveness of the proposed design schemes.     

受控Rabinovich系统的超混沌系统

在三维Rabinovich系统的基础上,通过引入一个线性状态反馈控制器构建一个新的四维超混沌系统,分析其基本动力学行为.在保证系统有界的前提下,通过计算Lyapunov指数值和研究其分岔的途径,证实其超混沌的特性.还给出了四维超混沌系统的指数吸引域和正向不变集等.同时也设计了实现四维Rabinovich超混沌吸引子的实际电路,验证了理论分析的结果.     

Study on the communication method for chaotic encryption in remote monitoring systems

In chaotic cryptosystems, it is recognized that using (very) high dimensional chaotic attractors for encrypting a given message may improve the privacy of chaotic encoding. In this paper, we study a kind of hyperchaotic systems by using some classical methods. The results show that besides the high dimension, the sub-Nyquist sampling interval (SI) is also an important factor that can improve the security of the chaotic cryptosystems. We use the method of time series analysis to verify the results.     

大数据加密算法在数据安全保护中的应用研究

针对大数据加密算法安全性不高,计算效率低等问题,本研究采用双混沌系统结合改进AES加密算法设计出一个混合加密算法,改进AES算是利用仿射变换对(A7、6F)生成新的S盒,采用的双四维超混沌系统是从两个三维混沌系统进行改造而成,然后利用改造后的超混沌系统生成混沌序列,设计出一个分组加密方案,在Hadoop大数据平台上,将双超混沌加密方案和改进的AES算法进行合并;试验表明,本研究的大数据加密算法安全性能高、密钥长度达688 bit,加密解密效率提高2倍以上.     

时变参数超混沌系统的同步方法与实现

提出了一种利用混沌映射产生的密钥序列控制混沌系统参数的新算法,并应用于四阶Lorenz超混沌系统,使系统能在混沌与超混沌状态随机的切换,仿真实验结果表明,证实了该方法在极大提高系统保密性的同时仍能很好保持系统的鲁棒性,为混沌同步保密通信的实用化提供了一种新方法。     

混沌系统的一种新指数同步方法及其在保密通信中的应用*

为了探索出一种新的指数同步方法,在已有研究的基础上,将一种非线性系统的指数稳定定理与李亚谱诺夫稳定性定理相结合,设计出一种合理的非线性控制器,理论上严格分析了该方法的可行性。以超混沌Chen系统为例,利用该方法实现了两个超混沌Chen系统的指数同步,并且同步性能优越。同时,将该方法应用到保密通信中,仿真结果显示发送端的信号能在接收端很好地被恢复出来,从而表明了该方法的有效性且在保密通信中有一定的应用前景。