非线性耦合分数阶系统的异结构同步

针对异结构的分数阶混沌系统同步问题,提出了非线性耦合分数阶异结构混沌系统的同步方法,即在α＋β-1=0条件下,利用非线性耦合实现两个异结构分数阶混沌系统同步,并通过数值仿真证明了其有效性.仿真实验显示,随着耦合系数的变化,系统呈现多样性,分数阶混沌系统出现不同混沌状态,而分数阶超混沌系统不仅会出现超混沌状态,还会出现发散的现象.     

论水文系统混沌特征的研究方向

简要介绍了混沌的概念，回顾了水文系统的混沌研究进展，从哲学上论证了水文系统混沌演化的普遍性，指出当前水文系统混沌研究的重点应该是探索水文系统混沌演化的普遍性，揭示水文系统混沌演化的成因机理和基本规律及其因果关系，提出了宏观、中观和微观时空尺度相结合，理论分析和计算机模拟相结合的水文系统混沌研究方法，讨论了形成混沌水文学的可能性     

Equilibrium regained: from nonequilibrium chaos to statistical mechanics

Far-from-equilibrium, spatially extended chaotic systems have generally eluded analytical solution, leading researchers to consider theories based on a statistical rather than a detailed knowledge of the microscopic length scales. Building on the recent discovery of a separation of length scales between macroscopic behavior and microscopic chaos, a simple far-from-equilibrium spatially extended chaotic system has been studied computationally at intermediate, coarse-grained scales. Equilibrium properties such as Gibbs distributions and detailed balance are recovered at these scales, which suggests that the macroscopic behavior of some far-from-equilibrium systems might be understood in terms of equilibrium statistical mechanics.     

耦合混沌系统完全同步的直接方法研究

为减少耦合误差,简化耦合函数的选择过程,提出一种实现耦舍混沌系统完全同步的直接方法,该方法不需将耦合误差系统进行近似的线性化处理,也不需要知道驱动系统状态变量的取值情况。只需根据驱动系统构造相应的耦舍函数,然后利用Routh判据确定待定耦合参数。以著名Lorenz系统为例说明了该方法的有效性。     

混沌系统的广义错位修正函数投影同步

首先介绍混沌系统的广义错位修正函数投影同步原理.然后根据驱动系统和响应系统维数的3种大小关系,选取驱动系统和响应系统,并根据Lyapunov稳定性方法构造响应系统的自适应控制器,实现驱动系统和受控响应系统的广义错位修正函数投影同步,数值仿真的结果表明了自适应控制器的正确性和有效性.最后计算广义错位修正函数投影同步混沌时间序列的近似熵,得出这样的同步混沌时间序列的复杂度更高,能够提高保密通信和图像加密的安全性.     

一类混沌系统的函数矩阵投影同步

研究了一类混沌系统的函数矩阵投影同步问题，基于函数矩阵方法，利用Lyapunov稳定性理论和极点配置理论，设计了两个连续混沌系统之间的同步方案，同时设计了两个离散混沌系统之间的同步方案，实现了驱动系统与动态系统按给定的函数矩阵投影同步，并给出了证明，通过对Lorenz混沌系统，和Henon系统的数值模拟，表明了该方法的有效性.     

基于T-S模糊模型的线性系统混沌反控制

研究了连续稳定线性系统的混沌反控制问题。基于T-S模糊模型表示的非线性混沌系统,实现了连续稳定线性系统的混沌化。此方法不需要计算系统的Liyapunov指数,大大降低了计算量。仿真结果表明了该方法的有效性。     

一种基于混沌同步的保密通信方案的设计

提出了一种新的基于混沌同步的保密通信方案。首先在发射端和接收端分别构建一个驱动系统及相应的响应系统。在发射端将信息信号调制到混沌变量中成为混沌传输信号,然后基于 Lyapunov 稳定性理论使两混沌系统达到同步,在接收端对混沌传输信号进行解调从而恢复出信息信号,混沌系统的初始条件和系统参数作为解调密钥。理论分析和数值仿真结果表明该方案是可行的。     

Chaos, symmetry, and self-similarity: exploiting order and disorder in mixing processes

Fluid mixing is a successful application of chaos. Theory anticipates the coexistence of order and disorder-symmetry and chaos-as well as self-similarity and multifractality arising from repeated stretching and folding. Experiments and computations, in turn, provide a point of confluence and a visual analog for chaotic behavior, multiplicative processes, and scaling behavior. All these concepts have conceptual engineering counterparts: examples arise in the context of flow classification, design of mixing devices, enhancement of transport processes, and controlled structure formation in two-phase systems.     

一种基于混沌同步的保密通信方案的设计

提出了一种新的基于混沌同步的保密通信方案。首先在发射端和接收端分别构建一个驱动系统及相应的响应系统。在发射端将信息信号调制到混沌变量中成为混沌传输信号,然后基于Lyapunov稳定性理论使两混沌系统达到同步,在接收端对混沌传输信号进行解调从而恢复出信息信号,混沌系统的初始条件和系统参数作为解调密钥。理论分析和数值仿真结果表明该方案是可行的。     

生态系统中浑沌现象的研究概况

就单种群、两种群和多种群三种情况,综述了浑沌现象的研究情况。结论是,从理论上讲,一些确定性系统在一定条件下可以表现出浑沌行为,同时讨论了对生态系统中浑沌现象研究的几种不同观点。认为浑沌是生态系统的一种重要现象,通过一定的方法(如拟合简单的差分方程模型、谱分析技术和相图重构技术)可以识别一些系统的浑沌行为。然而,方法本身还不十分完善,做出一个特定的自然生态系统是否存在浑沌这样的结论还需慎重。     

小麦条锈病受灾率时间序列混沌特征研究

利用混沌和分形理论,对湖北省襄樊地区小麦条锈病受灾率进行了混沌识别研究,对其功率谱、主分量、关联维度、最大Lyapunov指数进行了分析。结果表明,小麦条锈病受灾率时间序列具有混沌特征,属于混沌时间序列。因此建议对小麦条锈病进行建模预测时,应主要采用非线性建模方法。     

Stabilizing Lead-Salt Diode Lasers: Understanding and Controlling Chaotic Frequency Emission

Lead-salt tunable diode lasers (TDLs) are the only devices currently available that can generate tunable monochromatic radiation at arbitrary wavelengths between 3 and 30 micrometers and are particularly useful for high-resolution spectroscopy over a wide range of spectral regimes. Detailed observations of TDLs show that the observed instrumental linewidth is actually a temporal average of many narrow (less than 0.5 megahertz) emission "modes." The time scale characteristic of these "modes," which appear to be of relatively constant intensity, is of the order of a microsecond. The laser's behavior is highly suggestive of a chaotic process, that is, seemingly random excursions of a dynamic variable (frequency) within a bounded range. This report shows experimentally that TDL emissions are indeed chaotic. Furthermore, in a simple and robust fashion, this chaotic behavior has been successfully controlled with the use of recent techniques that take advantage of chaos to produce a narrow band laser output.     

Emerging coherence in a population of chemical oscillators

Coherence of interacting oscillating entities has importance in biological, chemical, and physical systems. We report experiments on populations of chemical oscillators and verify a 25-year-old theory of Kuramoto that predicts that global coupling in a set of smooth limit-cycle oscillators with different frequencies produces a phase transition in which some of the elements synchronize. Both the critical point and the predicted dependence of order on coupling are seen in the experiments. We extend the studies both to relaxation and to chaotic oscillators and characterize the quantitative similarities and differences among the types of systems.     

具有参数激励约简的扰动KdV方程的混沌行为

研究了具有参数激励约简的扰动KdV方程的混沌动力学行为.利用改进的Melnikov方法分析了由于同宿轨道的横截相交而产生的混沌行为.对周期外激励、周期线性参数激励和周期非线性参数激励下的扰动KdV方程的混沌行为进行了比较,发现划分混沌区与非混沌区的临界曲线是互不相同的.尤其是对非线性参数激励系统,存在"死频率".当这类系统受到该频率激励时,不论激励的振幅多大,混沌也不会发生.用时间积分法对上述系统进行了数值计算,结果与理论分析一致.     

耦合Brusselator振子的动力学行为研究

初步研究了由2个完全相同的 Brusselator 振子经过耦合组成的系统的动力学特征。研究结果表明,在较弱的耦合强度下,系统的动力学性质发生了根本性的变化,由混沌状态转变为周期性运动。不同于其他无延时耦合的系统,随着耦合强度的增强,系统又从周期运动转变为混沌运动。     

耦合Brusselator振子的动力学行为研究

初步研究了由2个完全相同的Brusselator振子经过耦合组成的系统的动力学特征。研究结果表明,在较弱的耦合强度下,系统的动力学性质发生了根本性的变化,由混沌状态转变为周期性运动。不同于其他无延时耦合的系统,随着耦合强度的增强,系统又从周期运动转变为混沌运动。     

计算机动态模拟方法在城市交通噪声监测中的应用

给出了通过几种经典的物理混沌系统，包括Chua’s电路、Lorenz系统、Chen系统，产生混沌随机序列的两种离散化方法.用NIST制定的测试标准对产生的随机序列进行了随机性统计测试分析.分别对不同的物理混沌系统产生的随机序列进行单比特频数测试、游程测试、离散傅里叶变换测试、近似熵测试、累积和测试，并进行了比较分析.实验结果表明：物理混沌序列要比算法混沌序列随机性更强，不同序列之间的随机性差异可以通过NIST测试得到体现.在三种经典电路中，建议选择Chen混沌系统的电路做为混沌随机序列发生器.     

一类改进的混沌时间序列局域非线性自适应预测

为了提高混沌时间序列的预测性能,在局域非线性自适应预测模型的非线性函数中引入参数,λ通过选择合适的λ建立新的非线性预测模型。通过对Logistic混沌映射、Henon混沌映射、Lorenz混沌流和Rosslor混沌流进行仿真计算,结果表明该模型的预测精度比局域非线性自适应预测的一步预测精度高,且具有一定程度的抗噪性能。     

Atmospheric dynamics of the outer planets

Despite major differences in the solar and internal energy inputs, the atmospheres of the four Jovian planets all exhibit latitudinal banding and high-speed jet streams. Neptune and Saturn are the windiest planets, Jupiter is the most active, and Uranus is a tipped-over version of the others. Large oval storm systems exhibit complicated time-dependent behavior that can be simulated in numerical models and laboratory experiments. The largest storm system, the Great Red Spot of Jupiter, has survived for more than 300 years in a chaotic shear zone where smaller structures appear and dissipate every few days. Future space missions will add to our understanding of small-scale processes, chemical composition, and vertical structure. Theoretical hypotheses about the interiors provide input for fluid dynamical models that reproduce many observed features of the winds, temperatures, and cloud patterns. In one set of models the winds are confined to the thin layer where clouds form. In other models, the winds extend deep into the planetary fluid interiors. Hypotheses will be tested further as observations and theories become more exact and detailed comparisons are made.