共轭Chen混沌系统的分岔分析及基于该系统的超混沌生成研究

分析了一个三维自治混沌系统的Hopf分岔现象,该系统的混沌吸引子属于共轭Chen混沌系统.通过引入一个控制器,基于该混沌系统构建了一个四维自治超混沌系统.该超混沌系统含有一个单参数,在一定的参数范围内呈现超混沌现象.通过Lyapunov指数和分岔分析,随着参数的变化该系统轨道呈现周期轨道、准周期轨道、混沌和超混沌的演化过程. 关键词： 混沌 超混沌生成 Hopf分岔 分岔分析     

A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system

This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms, and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis, the Hopf bifurcation processes are proved to arise at certain equilibrium points. Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours; the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally, an analog electronic circuit is designed to physically realize the chaotic system; the existence of four-wing chaotic attractor is verified by the analog circuit realization.     

Control and synchronization of a hyperchaotic system based on passive control

In this paper, a new hyperchaotic system is proposed, and the basic properties of this system are analyzed by means of the equilibrium point, a Poincar map, the bifurcation diagram, and the Lyapunov exponents. Based on the passivity theory, the controllers are designed to achieve the new hyperchaotic system globally, asymptotically stabilized at the equilibrium point, and also realize the synchronization between the two hyperchaotic systems under different initial values respectively. Finally, the numerical simulation results show that the proposed control and synchronization schemes are effective.     

Controlling and synchronization of a hyperchaotic system based on passive control

In this paper, a new hyperchaotic system is proposed, and the basic properties of this system are analyzed by means of equilibrium point, Poincaré map, bifurcation diagram, and Lyapunov exponents. Based on the passivity theory, the controllers are designed to achieve the new hyperchaotic system globally, asymptotically stabilized at the equilibrium point, and also realize the synchronization between the two hyperchaotic systems under different initial values respectively. Finally, the numerical simulation results show that the proposed control and synchronization schemes are effective.     

一种新的三维自治混沌系统

通过对蔡氏电路的研究,提出了一种新的混沌系统,并对该系统的基本动力学特性进行了深入研究,得到该系统的Lyapunov指数和Lyapunov维数,给出了相图、Lyapunov指数谱、分岔图、Poincaré映射以及功率谱等.利用OrCAD-PSpice软件设计了该新混沌系统的振荡电路并进行了仿真实验.研究结果表明,该系统与蔡氏电路产生的混沌吸引子并不拓扑等价,且该系统的参数变化范围较大,最大Lyapunov指数接近1,数值仿真和电路系统实验仿真具有很好的一致性,证实了该系统的存在性和物理上可实现性. 关键词： 混沌系统 Lyapunov指数谱 分岔图 电路实现     

四维切换超混沌系统

构建了一类关联且有多种切换方式的四维超混沌系统.依据系统的分岔图确定了各个子系统都处于混沌状态时，系统参数的取值范围.分析了这类四维超混沌系统平衡点的性质、超混沌吸引子的相图和Lyapunov指数等特性，设计了实现这类可切换超混沌系统的实际电路，利用系统选择器，一个电路可以实现四个关联子系统的功能. 关键词： 超混沌系统 分岔图 Lyapunov指数 切换     

一个三维四翼自治混沌系统的拓扑马蹄分析

基于拓扑马蹄映射理论,验证了一个三维四翼自治的混沌系统的拓扑马蹄的存在.由于该混沌系统是连续系统,首先选取了一个Poincaré截面,并在该截面下定义了该混沌系统的一个一次回归Poincaré映射.通过利用计算机辅助证明方法,得出了该映射与一个2移位映射拓扑半共扼,说明该三维四翼自治系统的拓扑熵大于或等于ln2,进而证明了该系统的混沌行为. 关键词： 四翼混沌系统 拓扑马蹄 Poincaré映射 拓扑熵     

Generation of a novel spherical chaotic attractor from a new three-dimensional system

A new three-dimensional （3D） system is constructed and a novel spherical chaotic attractor is generated from the system. Basic dynamical behaviors of the chaotic system are investigated respectively. Novel spherical chaotic attractors can be generated from the system within a wide range of parameter values. The shapes of spherical chaotic attractors can be impacted by the variation of parameters. Finally, a simpler 3D system and a more complex 3D system with the same capability of generating spherical chaotic attractors are put forward respectively.     

一个分数阶新超混沌系统的同步

研究了分数阶混沌系统的同步问题,以分数阶新超混沌系统为例,设计了三种同步方法,运用拉普拉斯变换理论和分数阶线性稳定理论给以证明,数值仿真或电路仿真证实了所提同步方法的有效性和可行性. 关键词： 分数阶 混沌同步 新超混沌系统     

关联可切换超混沌系统的构建与特性分析

利用拓展系统变量,增加系统的非线性函数和对原系统实施反混沌控制方法,构建了一类关联且有多种切换方式的超混沌系统,对这类系统的分岔图、平衡点的稳定性、Lyapunov指数和动力学行为的演化过程进行了分析.设计了实现切换超混沌系统的电路,利用开关的切换,一个电路能实现多个超混沌系统的功能. 关键词： 超混沌系统 切换 分岔图 Lyapunov指数     

一个新分数阶超混沌系统及其混沌同步

给出了一个新的分数阶超混沌系统,利用严格数学理论实现了该分数阶超混沌系统的混沌同步,在同步过程中并未删除响应系统的非线性项,理论分析与仿真计算表明了同步方法的有效性. 关键词： 分数阶超混沌系统 混沌同步 非线性项     

超混沌Chen系统和超混沌Roessler系统的异结构同步

用两种不同的方法——主动控制同步法和自适应控制同步法实现超混沌Chen系统和超混沌Roessler系统的异结构同步，各自设计了不同的控制器，使得响应系统与驱动系统同步．当参数已知时，采用主动控制法，方法简单有效且不需要构造Lyapunov函数，实现同步的时间短；当系统参数未知或结构不确定时，基于Lyapunov稳定性理论，给出自适应同步控制器的系统设计过程和参数自适应律，使得系统达到同步同时识别未知参数，数值模拟验证了两种方法的有效性。     

快慢型超混沌Lorenz系统分析

讨论了快慢两时间尺度下超混沌Lorenz系统原点的稳定性问题,分析了原点的Hopf分岔,包括Hopf分岔的存在性,分岔方向以及分岔周期解的稳定性等问题,并用数值例子对所得到的结果加以验证.在一定的参数条件下,快慢系统会产生对称簇发并能达到超混沌状态.基于快慢分析法,揭示了对称簇发中沉寂态与激发态相互转迁的不同分岔模式,并进一步分析了耦合强度对慢过效应的影响. 关键词： 超混沌Lorenz系统 Hopf分岔 对称式fold/subHopf簇发 慢过效应     

Control of fractional chaotic and hyperchaotic systems based on a fractional order controller

We present a new fractional-order controller based on the Lyapunov stability theory and propose a control method which can control fractional chaotic and hyperchaotic systems whether systems are commensurate or incommensurate.The proposed control method is universal, simple, and theoretically rigorous. Numerical simulations are given for several fractional chaotic and hyperchaotic systems to verify the effectiveness and the universality of the proposed control method.     

一种基于超混沌系统的立体图像零水印算法

为了在不改变立体图像质量的前提下对立体图像实施版权保护,提出了一种基于超混沌离散系统的立体图像零水印算法. 该算法利用立体图像左右视点小波变换域低频子带视差的稳定性以及离散余弦变换直流系数稳定的特点构造了一种视差零水印. 在水印构造过程中,利用了超混沌离散系统的初始值敏感性、参数密钥空间大和动力学行为复杂等特性映射视差零水印的 位置信息,从而增强了水印算法的安全性.此外,还分析了水印安全性与水印容量之间的关系. 实验结果表明,该立体图像视差零水印算法对加噪、滤波、压缩、剪切、图像放大和缩小等各种对称和非对称攻击表现出了 较强的鲁棒性.     

三维超混沌映射拓扑马蹄寻找算法及应用

拓扑马蹄理论是严格研究混沌的重要理论,然而却很少用在超混沌的研究中.主要原因是超混沌系统不仅相空间维数比普通混沌高,而且存在的拉伸方向数也较多,导致拓扑马蹄的寻找难度很大.为此,本文针对三维超混沌映射,提出一种实用的拓扑马蹄寻找算法.超混沌系统通常有较大的负Lyapunov指数,其吸引子会靠向某一曲面.基于这种特性,本文首先沿着系统收缩方向进行降维,得出二维平面投影系统;接着在新系统中搜索二维拉伸的投影马蹄;最后利用投影马蹄升维构造出原三维系统拓扑马蹄.为了验证算法的有效性,本文以经典Lorenz超混沌系统和著名Saito超混沌电路为例,利用数值计算,在它们的Poincare映射中找出了具有二维拉伸的三维拓扑马蹄.     

A new image encryption algorithm based on fractional-order hyperchaotic Lorenz system

We propose a new image encryption algorithm on a basis of the fractional-order hyperchaotic Lorenz system. While in the process of generating a key stream, the system parameters and the derivative order are embedded in the proposed algorithm to enhance the security. Such an algorithm is detailed in terms of security analyses, including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. The experimental results demonstrate that the proposed image encryption scheme has the advantages of large key space and high security for practical image encryption.     

A novel fractional-order hyperchaotic system and its synchronization

In this paper,a novel hyperchaotic system with one nonlinear term and its fractional order system are proposed.Furthermore,synchronization between two fractional-order systems with different fractional-order values is achieved.The proposed synchronization scheme is simple and theoretically rigorous.Numerical simulations are in agreement with the theoretical analysis.     

Anti-synchronization of a new hyperchaotic system via small-gain theorem

Based on the small-gain theorem, the anti-synchronization between two identical new hyperchaotic systems is investigated, moreover, the general sufficient conditions to achieve anti-synchronization between the new hyperchaotic system and the new hyperchaotic Lorenz system are obtained via small-gain theorem. Numerical simulations are performed to verify and illustrate the analytical results.     

基于同相第二代电流传输器的网格多涡卷混沌电路研究

通过简化广义Jerk系统,构建了一个三维网格多涡卷混沌系统,利用同相第二代电流传输器(CCII+)设计并实现了该系统的模拟电路,将该电路与传统运放实现的混沌电路进行了对比,发现基于CCII+的混沌电路能在更高频段产生网格多涡卷吸引子,且电路结构更简单,使用器件更少,最后,通过示波器观测到了网格多涡卷混沌吸引子,验证了混沌电路的物理可实现性,电路实验结果与数值仿真结果一致。