一种新型量化混沌序列的统计特性研究

提出了一种多值量化器，并对一维无限折叠混沌映射所产生的多值量化序列的统计特性与混沌映射和量化器参数的关系进行了研究。理论分析和统计检验表明，选择适当的参数可使量化序列接近于独立同分布序列。该多值序列发生器还具有结构简单、实现效率高等优点。因此，它可用于产生混沌扩谱序列和混沌密钥流序列。     

纳米系统的反控制片时混沌

通过设计由经典混沌映射所表示的按时驱动能够实现纳米系统的片时混沌。本文应用子动力学理论相应给出了演化算子一般性的谱分解,然后给出了应用一维混沌映射驱动原始系统进入片时混沌的步骤。给出了量子点系统表现反控制和同步片时混沌的相应的计算。     

混沌挤出过程相空间动力学行为分析与表征

根据对称性与周期性,建立了混沌螺杆螺槽的混合过程动力学模型。采用有限体积方法,得到一个周期长度速度场数值解,将结果映射到3个周期长度的相空间内对混沌混合过程动力学进行分析与表征。结果表明,常规的层流混合和混沌混合区域共存,两种混合区域通过"8"字型同宿轨道包围的KAM岛分割开来,内部为常规混合区域,外围为混沌混合区域。示踪粒子在三维重构的相空间内动力学行为清楚地刻画了系统向混沌进发的过程及速度。另外,由于长度有限,混沌混合的作用受到限制,不再具有无穷的自相似结构,可以采用KAM岛的区域大小来表征混合。     

硬刚度特性非线性隔振系统分叉的数值研究

倍周期分叉是通向混沌的主要道路之一，而现有的分析方法对进行硬刚度特性非线性振动系统的分叉分析存在着诸多局限，因此，应用数值方法研究其分叉具有重要意义。本文通过Poincare映射方法得出硬刚度特性非线性隔振系统的全局分叉图，然后通过胞映射方法分析其静态和动态分叉。     

一个新的混沌映射及其算法实现

给出了一个新的混沌映射-网状映射的解析表达式及其图形,将其同传统的Logistic映射以及Mandness曲线、神经网络所产生的吸引子的图形进行了比较,从图形学的角度对其形态进行了分析。给出了由该网状混沌所派生出米的一些例子。本义的工作对利用分形进行动植物模拟以及分形艺术的创造有重要的参考意义和应用价值,对混沌动力系统的研究也提供了一种新的途径。     

基于动态可变参数的复合混沌系统的语音加密算法研究

利用混沌理论,基于Hénon映射和Logistic映射设计了一个复合混沌系统,并证明了其具有更好的初值敏感性。对产生的混沌二值序列进行美国国家标准与技术研究所(National Institute of Standard and Technology,NIST)随机数测试,分析得出该序列具有较好的随机性,可用于加密。依此设计了一个语音加密算法,实现了语音信号的加/解密功能。仿真分析表明,该混沌语音加密算法具有较高的安全性,能产生足够的密钥空间,有较强的保密性能。     

压缩映射-参数微扰控制混沌

提出一个压缩映射-参数微扰控制混沌动力特性的新方法，通过对系统可调参数的瞬态小干扰反馈，将非线性动力系统中出现的混沌运动，引导到嵌入在混沌吸引子内无数不稳定周期轨中预期的一个轨，并使之稳定。本方法用于控制非线性转子系统和Duffing振子系统的混沌运动、数值结果表明该方法有效。     

两类受迫Duffing方程混沌解的图形化比较

Duffing方程是常微分方程理论研究中比较有代表性的非线性系统之一。笔者通过运用数值计算可视化和解析分析方法,对两类受迫Duffing方程的混沌解进行图形化研究,揭示了Duffing系统在不同强弱激励下混沌表现的不同:强激励下系统的混沌吸引子在Poincaré映射图上具有明显自相似的分形结构,而弱激励下则呈现出模糊状态。并进一步对混沌吸引子结构形态的差异进行了比较和分析,利用耗散结构理论对产生差异的原因进行了合理解释。     

Henon映射的图像加密新算法

从混沌动力学的角度出发,运用非线形控制系统的原理来研究混沌序列.以Henon映射为基础,在控制系统设置控制参数以形成混沌序列.同时也证明了模加减运算是成立的,并给出了相应定理的证明.在图像加密新算法中,运用了异或运算和模加减运算相结合的方式.实验结果证明,该算法生成的混沌序列对图像加密具有比较好的效果.     

基于DSP Builder的混沌扩频序列的生成

扩频通信系统在用的m序列和Gold序列,存在序列长度有限和数量有限等缺陷.连续混沌系统经离散化可以产生长度非常大的序列和数目巨大的码元,这样混沌所产生扩频伪随机码在扩频通信领域表现出比传统扩频码更好的相关特性和误码特性,使频谱资源得到充分利用.我们设计个混沌电路.进行电路实现,经离散化后得到具有良好相关特性的混沌扩频序列.     

Parametric transverse patterns in broad aperture lasers

Parametrically generated optical patterns are investigated for finite and large-scale transverse aperture lasers. Standing and rotating patterns as well as periodic and chaotic pattern alternations are described in the framework of the amplitude equation formalism. Sensitive dependence on the geometrical size of the system is demonstrated even in the case of large-scale systems     

Anti-integrability in scattering billiards

Examples that scattering billiards exhibit anti-integrability are shown. A Cantor set can be constructed such that the generalized Sinai billiard map under consideration restricted to it is conjugate to a subshift of finite type with a given number of symbols. The chaotic and Bernoulli properties are inherited from the 'δ-billiards'.     

基于素数的混沌伪随机数发生器的安全性分析

分析了一类基于素数的混沌伪随机数发生器的安全性问题。分析表明，此类混沌伪随机数发生器的输出不是密码学安全的伪随机序列，在截获不长的一段序列的基础上即可很容易地恢复此类PRNGs的全部密鲷。虽然基于素数的方法在改善混沌序列相关性能、周期长度等方面具有一定的优势，但是却不能增加序列的不可预测性，这就限制了此类混沌伪随机数发生器在诸多应用领域中的应用前景。     

Molecular dynamics simulation of transition metal cluster fragmentation and recombination

Fragmentation of transition metal clusters at finite temperature due to a high-energy excitation was studied by molecular dynamics and Monte Carlo simulation. The process is found to be chaotic, with high sensitivity to initial conditions, and the fragment distribution is consistent with power-law behavior. Recombination of the fragments was attempted and observed to occur only infrequently, with large, liquid fragments being a necessary but not sufficient condition for successful re-assembly.     

具有输入死区的分数阶Victor-Carmen系统的有限时间同步（英）

有限时间控制能获得更快的收敛速度,是一种有效的控制策略．混沌系统有限时间同步明显优于渐近同步．本文研究了具有输入死区的分数阶Victor-Carmen系统的有限时间同步问题,为了使Victor-Carmen系统在给定时间内收敛到平衡点,提出了一种自适应滑模控制策略．设计了一种非奇异分数阶滑模面,为了将同步误差系统的轨迹驱动到滑模面上引入了自适应滑模控制律,实现了主从系统的混沌同步．通过算例说明了所提出的有限时间控制器的有效性和适用性,并验证了本文的理论结果．     

An evaluation of the Lyapunov characteristic exponent of chaotic continuous systems

A procedure to calculate the Lyapunov characteristic exponent of the response of structural continuous systems, discretized using finite element methods, is proposed. The Lyapunov characteristic exponent can be used to characterize the asymptotic stability of the system dynamic response, and it is frequently employed to identify a chaotic behaviour. The proposed procedure can also be used in the stability characterization of fluid–structure interaction systems in which the focus of the analysis is on the behaviour of the structural part. Copyright © 2002 John Wiley & Sons, Ltd.     

Chaotic double cycling

We study the dynamics of a generic vector field in the neighbourhood of a heteroclinic cycle of non-trivial periodic solutions whose invariant manifolds meet transversely. The main result is the existence of chaotic double cycling: there are trajectories that follow the cycle making any prescribed number of turns near the periodic solutions, for any given bi-infinite sequence of turns. Using symbolic dynamics, arbitrarily close to the cycle, we find a robust and transitive set of initial conditions whose trajectories follow the cycle for all time and that is conjugate to a Markov shift over a finite alphabet. This conjugacy allows us to prove the existence of infinitely many heteroclinic and homoclinic subsidiary connections, which give rise to a heteroclinic network with infinitely many cycles and chaotic dynamics near them, exhibiting themselves switching and cycling. We construct an example of a vector field with Z ₃ symmetry in a five-dimensional sphere with a heteroclinic cycle having this property.     

Phase-space prediction of chaotic time series

We report on improved phase-space prediction of chaotic time series. We propose a new neighbour-searching strategy which corrects phase-space distortion arising from noise, finite sampling time and limited data length. We further establish a robust fitting algorithm which combines phase-space transformation, weighted regression and singular value decomposition least squares to construct a local linear prediction function. The scaling laws of prediction error in the presence of noise with various parameters are discussed. The method provides a practical iterated prediction approach with relatively high prediction performance. The prediction algorithm is tested on maps (Logistic, Hénon and Ikeda), finite flows (Rössler and Lorenz) and a laser experimental time series, and is shown to give a prediction time up to or longer than five times the Lyapunov time. The improved algorithm also gives a reliable prediction when using only a short training set and in the presence of small noise.     

Towards a classification of generic bifurcations in dissipative dynamical systems

A new matrix classification of the eighteen well-documented generic codimension-one bifurcations of dissipative dynamical systems is presented, based on the embedding dimensions of the attractors before and after the events. Global as well as local bifurcations of point, cycUc, toroidal and chaotic attractors are all embraced by the scheme. Focussing attention on control changes in the direction of increasing complexity of the attracting set, the distance from the leading diagonal is a useful practical measure of the severity ofthe instability. Subtle (continuous) and catastrophic (discontinuous) bifurcations are distinguished. The former are associated with safe boundariesin the control space, while the latter are subdivided into explosive boundaries that cause a sudden finite enlargement (explosion) of the attracting set, and dangerous boundaries that cause a sudden finite jump in observed behaviour by .virtue of the complete blue-sky disappearance of the attractor.     

5种新混沌弱信号检测系统设计

为了进一步改进混沌弱信号检测系统的性能,设计了5种新的高灵敏度复合混沌弱信号检测系统,并选择其中一种与目前广泛使用的Duffing混沌弱信号检测系统进行了对比分析,结果显示新复合混沌系统可以克服Duffing混沌弱信号检测系统出现的3个难题:被检测信号消失后混沌状态无法快速自动回复、大周期状态不稳定以及混沌状态和大周期状态难以区分。通过使用Jacobian矩阵和特征方程的分析,显示了新复合混沌系统比Duffing混沌系统更为有效。与传统弱信号检测方法相比,新复合混沌系统电路简单、具有更低的信噪比和检测信号门限。理论分析和实验显示了新复合混沌系统的特性。