一个全局耦合不连续映像格子中的奇异态

文章研究了一类由既不可逆又不连续映像构成的全局耦合映像格子系统中的奇异态行为,计算了系统的同步序参量和空间振幅变化图.结果表明,在某些特定的参数区间内,耦合映像格子系统会出现奇异态或团簇态,并且敏感地依赖于耦合强度的选择.上述丰富的动力学现象是由于单映像中不连续、不可逆性以及空间耦合相互作用的结果.通过数值模拟找到了奇异态或团簇态出现的特定参数区域.     

Lorenz系统驱动声光双稳时空混沌系统并行同步的研究

研究了一个时间混沌系统驱动多个时空混沌系统的并行同步问题.以单模激光Lorenz系统和一维耦合映像格子为例,在单模激光Lorenz系统中提取一个混沌序列,通过与一维耦合映像格子中的状态变量耦合使单模激光Lorenz系统和多个同结构一维耦合映像格子同时达到广义同步,并且多个一维耦合映像格子之间实现完全并行同步.通过计算条件Lyapunov指数,可以得到并行同步所需反馈系数的取值范围.数值模拟证明了此方法的可行性和有效性.     

基于符号动力学的耦合映像格子系统的初值估计

在符号动力学的基础上,深入探讨了基于动力学符号序列的局部耦合映像格子系统求逆问题.在理论上系统地分析耦合映像系统初值估计的性能与耦合系数及映射函数之间的数学关系,证明相空间I^M上的任意取值通过基于符号向量序列的逆迭代过程并不一定收敛至初值,其敛散性与耦合强度和映射函数的选择有直接关系.同时证明了混沌或其拓扑共轭的逆不一定为压缩映射,其总体的敛散性与整个逆迭代过程中的收敛与发散的强度对比有关.理论分析与数值实验结果完全一致,说明本文提出的耦合映像格子系统初值估计问题的分析 关键词： 耦合映像格子 符号动力学 初值估计     

化学自催化混沌反应模型中的耦合作用与混沌同步

选用混沌自催化反应作为子系统 ,构造了耦合自催化反应系统 ,研究了耦合变量、耦合系数对混沌动力学行为的影响 ,给出了不同耦合系数下系统的动力学特征 ,探讨了耦合作用机制 .结果表明 ,耦合作用能明显地改变子系统的动力学行为 ,强化系统间的相关性 .耦合后的混沌运动受到调整与抑制 ,耦合强度加大时 ,呈现出混沌运动轨线的周期化 ,耦合系数大于临界值 ,两子系统实现了完全的同步 .不同变量的耦合时 ,影响最大的是第二种变量 .对于三种物质均有耦合时 ,更容易出现混沌的抑制、运动状态的锁相与周期化和混沌的完全同步 .     

一类时空混沌加解密系统的安全分析

本文安全分析文献 所提的一类自同步的时空混沌流密码系统.发现该高维的加解密系统在常数的驱动下将收敛到一维,使得动力学系统的复杂性大为降低.在某些特定输入区域内容,保密系统对输入状态的微小扰动不敏感.可以建立密钥和特殊输入状态间一个简单的线性关系,并依次从密钥流中恢复出密钥.基于此,提出一套选择密文攻击方法,利用系统参数和扰动前后密钥流的差异之间的依赖关系通过寻优算法破解密钥,从而攻击了上述文献所提出的基于混沌自同步的安全通信算法. 关键词： 混沌密码 耦合映像格子 安全分析     

耦合映像格子中时空混沌的状态反馈控制

利用状态反馈的方法，实现了耦合映像格子中时空混沌的稳定控制.反馈方式可以是没有延迟的，也可以是有延迟的；控制方式可以是连续的，也可以是脉冲的.数值模拟结果证明了状态反馈方法的有效性. 关键词： 耦合映像格子 时空混沌 状态反馈控制     

基于符号向量动力学的耦合映像格子参数估计

本文,将符号动力学推广到耦合映像格子中,以Logistic映射下耦合映像格子为研究对象,研究控制参数对符号向量序列动力学特性的影响.通过研究耦合映像格子逆函数,给出耦合映像格子的遍历条件.进一步,将给出系统初始向量,禁止字以及控制参数的符号向量序列描述方法,并最终给出基于符号向量动力学的耦合映像格子控制参数估计方法.实验结果表明,根据本文算法可以有效建立符号序列和耦合映像格子控制参数之间的对应关系,能够更好地刻画了实际模型的物理过程. 关键词： 符号向量动力学 耦合映像格子 参数估计 遍历性     

基于多重耦合映像格子的信号初值恢复研究

利用耦合映像格子恢复信号初值是信号处理研究中一个重要的问题.耦合映像格子具有混沌系统的初值敏感性，当初值受到噪声污染时将会影响到系统对其的恢复.提出了一种由多个一维耦合映像格子系统并列耦合而成的多重耦合映像格子系统，通过将多个一维系统耦合，使因受到噪声干扰而趋向于指数分离的混沌轨道相互靠近，以达到抑制噪声的目的.数值仿真表明，该系统具有较强的抗噪声能力和较高的鲁棒性.在耦合系数选取适当的情况下，即使初始信号受到噪声干扰，该多重耦合系统仍然能够很好地恢复信号初值的统计特性，且对单个初值的恢复情况及与初始信号 关键词： 耦合映像格子 恢复信号的统计特性 多重耦合     

基于可变参数双向耦合映像系统的时空混沌Hash函数设计

在分析单向与双向耦合映像格子系统的初值与参数敏感性的基础上，提出了一种基于可变参数双向耦合映像系统的时空混沌单向Hash函数构造方案.该方案以耦合映像系统的部分初态作为密钥，在迭代过程中, 通过上一次的迭代值和线性变换后的不同位置的明文消息比特动态确定双向耦合映像系统模型参数，将明文消息多格点并行注入时空混沌轨迹中；取迭代序列中最后一轮迭代结果的适当空间项，线性映射为Hash值要求的128 bit值.由于耦合映像系统的双向扩散机理与混乱作用，迭代过程具有极强的不可逆性及初值与参数敏感性，Hash结果的每位都与明文及密钥有着敏感、复杂的非线性强耦合关系.仿真实验与分析结果表明，该算法达到了Hash函数的各项性能要求，安全性好，执行效率高. 关键词： Hash函数 时空混沌 耦合映像格子     

混沌加密的虹膜识别系统的安全性

提出了针对特征码的单向耦合映像格混沌加密系统,以及Arnold变换与单向耦合映像格混沌系统相结合对虹膜信息进行加密的复合混沌加密系统.利用Arnold变换置乱并混淆虹膜图像,通过镜像解决零点不变性问题,最后通过单向耦合映像格混沌系统实现加密.实验表明本算法密钥空间大,统计特性好,密钥敏感性强,加密速度快,平均加密时间70 ms.     

Collective behavior in coupled chaotic map lattices with random perturbations

Numerical simulations of coupled map lattices with non-local interactions (i.e., the coupling of a given map occurs with all lattice sites) often involve a large computer time if the lattice size is too large. In order to study dynamical effects which depend on the lattice size we considered the use of small truncated lattices with random inputs at their boundaries chosen from a uniform probability distribution. This emulates a “thermal bath”, where deterministic degrees of freedom exhibiting chaotic behavior are replaced by random perturbations of finite amplitude. We demonstrate the usefulness of this idea to investigate the occurrence of completely synchronized chaotic states as the coupling parameters are varied. We considered one-dimensional lattices of chaotic logistic maps at outer crisis x→4x(1−x).     

基于符号向量动力学的耦合映像格子初始向量估计

在符号动力学的基础上,探讨了基于符号向量序列的局部耦合映像格子求逆问题,证明了相空间I^N上任意取值通过基于符号向量序列的逆迭代过程必然收敛至初始向量,提出了基于符号向量动力学的初始向量估计算法,从而建立了耦合映像格子符号序列和实际动力系统相空间的对应关系.实验结果表明,根据该算法可以有效建立符号向量序列和耦合映像格子相空间之间的对应关系,更好地刻画了实际模型的物理过程. 关键词： 耦合映像格子 符号动力学 初始向量估计     

Controllable coupling and quantum correlation dynamics of two double quantum dots coupled via a transmission line resonator

We propose a theoretical scheme to generate a controllable and switchable coupling between two double-quantum-dot (DQD) spin qubits by using a transmission line resonator (TLR) as a bus system. We study dynamical behaviors of quantum correlations described by entanglement correlation (EC) and discord correlation (DC) between two DQD spin qubits when the two spin qubits and the TLR are initially prepared in X-type quantum states and a coherent state, respectively. We demonstrate that in the EC death regions there exist DC stationary states in which the stable DC amplification or degradation can be generated during the dynamical evolution. It is shown that these DC stationary states can be controlled by initial-state parameters, the coupling, and detuning between qubits and the TLR. We reveal the full synchronization and anti-synchronization phenomena in the EC and DC time evolution, and show that the EC and DC synchronization and anti-synchronization depends on the initial-state parameters of the two DQD spin qubits. It is shown that the initial quantum correlation may be suppressed completely when the evolution time approaches to the infinity in the presence of dissipation. These results shed new light on dynamics of quantum correlations.     

Effects of randomness on chaos and order of coupled logistic maps

Natural systems are essentially nonlinear being neither completely ordered nor completely random. These nonlinearities are responsible for a great variety of possibilities that includes chaos. On this basis, the effect of randomness on chaos and order of nonlinear dynamical systems is an important feature to be understood. This Letter considers randomness as fluctuations and uncertainties due to noise and investigates its influence in the nonlinear dynamical behavior of coupled logistic maps. The noise effect is included by adding random variations either to parameters or to state variables. Besides, the coupling uncertainty is investigated by assuming tinny values for the connection parameters, representing the idea that all Nature is, in some sense, weakly connected. Results from numerical simulations show situations where noise alters the system nonlinear dynamics.     

Oscillation death in coupled oscillators

We study dynamical behaviors in coupled nonlinear oscillators and find that under certain conditions, a whole coupled oscillator system can cease oscillation and transfer to a globally nonuniform stationary state [i.e., the so-called oscillation death (OD) state], and this phenomenon can be generally observed. This OD state depends on coupling strengths and is clearly different from previously studied amplitude death (AD) state, which refers to the phenomenon where the whole system is trapped into homogeneously steady state of a fixed point, which already exists but is unstable in the absence of coupling. For larger systems, very rich pattern structures of global death states are observed. These Turing-like patterns may share some essential features with the classical Turing pattern.      

Discrete-time quantum walks on one-dimensional lattices

In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattices, we derive an explicit expression for the return probability, which shows scaling behavior P(0, t) ~ t ^-1 and does not depends on the initial states of the walk. In the long-time limit, the probability distribution shows various patterns, depending on the initial states, coin parameters and the lattice size. The time-averaged probability mixes to the limiting probability distribution in linear time, i.e., the mixing time M _ε is a linear function of N (size of the lattices) for large values of thresholds ϵ. Finally, we introduce another kind of quantum walk on infinite or even-numbered size of lattices, and show that by the method of mathematical induction, the walk is equivalent to the traditional quantum walk with symmetrical initial state and coin parameter.     

Evaluating the dynamical coupling between spatiotemporally chaotic signals via an information theory approach

An information-theoretic measure is introduced for evaluating the dynamical coupling of spatiotemporally chaotic signals produced by extended systems. The measure of the one-way coupled map lattices and the one-dimensional, homogeneous, diffusively coupled map lattices is computed with the symbolic analysis method. The numerical results show that the information measure is applicable to determining the dynamical coupling between two directly coupled or indirectly coupled chaotic signals.     

Robustness and Flexibility of Neural Function through Dynamical Criticality

In theoretical biology, robustness refers to the ability of a biological system to function properly even under perturbation of basic parameters (e.g., temperature or pH), which in mathematical models is reflected in not needing to fine-tune basic parameter constants; flexibility refers to the ability of a system to switch functions or behaviors easily and effortlessly. While there are extensive explorations of the concept of robustness and what it requires mathematically, understanding flexibility has proven more elusive, as well as also elucidating the apparent opposition between what is required mathematically for models to implement either. In this paper we address a number of arguments in theoretical neuroscience showing that both robustness and flexibility can be attained by systems that poise themselves at the onset of a large number of dynamical bifurcations, or dynamical criticality, and how such poising can have a profound influence on integration of information processing and function. Finally, we examine critical map lattices, which are coupled map lattices where the coupling is dynamically critical in the sense of having purely imaginary eigenvalues. We show that these map lattices provide an explicit connection between dynamical criticality in the sense we have used and “edge of chaos” criticality.     

Analysis of convergence for initial condition estimation of coupled map lattices based on symbolic dynamics

A novel approach to the inverse problem of diffusively coupled map lattices is systematically investigated by utilizing the symbolic vector dynamics.The relationship between the performance of initial condition estimation and the structural feature of dynamical system is proved theoretically.It is found that any point in a spatiotemporal coupled system is not necessary to converge to its initial value with respect to sufficient backward iteration,which is directly relevant to the coupling strength and local mapping function.When the convergence is met,the error bound in estimating the initial condition is proposed in a noiseless environment,which is determined by the dimension of attractors and metric entropy of the system.Simulation results further confirm the theoretic analysis,and prove that the presented method provides the important theory and experimental results for better analysing and characterizing the spatiotemporal complex behaviours in an actual system.