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A methodology of noise-like key generation is presented. Chaotic process of tentmap function is used as a deterministic generation of noise-like key, image storage and retrieval are completed in a algebraic form. A mathematics model of noise-like chaotic coding memory is constructed, meanwhile the basic mechanism of circulant convolution and circulant correlation in image information storage and retrieval are demonstrated.

在详细阐明数字序列和字母序列的1-D映射函数设计方法的基础上，利用构造出的1-D映射的稳定周期环和不稳定极限环完成了存储和联想记忆功能，为了识别有关的输入信息，提出了映射函数直接控制的方法；在此基础上，提出了一种1-D映射型混沌神经网络模型，该网络本身不当作一个"黑箱"处理，网络的参数值由网络中实现的映射函数来确定，该网络模型具有联想记忆、容错性、模式识别和奇异滤波等一系列智能信息处理的基本功能。

Based on global coupling, a method which can induce both synchronization and anti-synchronization by constructing coupled chaotic system with identical antisymmetric chaotic systems was presented.

提出在具有反对称性的等同混沌子系统中，利用全局耦合实现同步与反同步共存的一般方法，论证了其在离散系统和连续系统上的适用条件。

We have studied the chaotic neural networks and the phase spaceprediction model based on chaotic attractor.

本文研究了混沌学习算法神经网络的预测性能和基于混沌吸引子的相空间预测模型。

Based on the delay-coordinate reconstruction and bilinear expressions in the phase space of a chaotic system, a bilinear adaptive filter was designed to predict low-dimensional chaotic time series.

基于混沌动力系统相空间的延迟坐标重构和双线性表达式，设计了预测混沌时间序列的双线性自适应预测滤波器。

Then, introducing the improved straight-line stabilization method to control the chaotic phenomena in the models, a controller is designed to stabilize the biological population in the oribits where the fixed points lie on, thus eliminating the chaotic phenomena in population to keep the population system in persistent existence.

其次采取改进的直线稳定化方法控制模型所存在的混沌现象，设计并求得了使得生物种群稳定到不动点轨道的控制器，最终消除了种群中存在的混沌现象，从而保持了种群系统的持续生存。

The characteristic exponent based on a probabilistic dynamical system is calculated, which provides some useful information on unstable periodic orbits of the chaotic economic dynamical system. An effective controlling parameter is chosen by discussing the sign of the characteristic exponent. Furthermore, the control regions of the parameter variable are proposed. Therefore the controllable domain of chaos in the chaotic economic model can be obtained.

提出一种等价关系，计算基于概率的动力系统的特征指数，给出混沌经济动力系统的不稳定周期轨道的有用信息，通过讨论特征指数的符号，选择有效的控制参数，得到相应的控制参数取值范围，从而得到混沌经济模型中的参数变量的混沌控制域。

Based on the equilibrium equation of an arch element the cubic nonlinear dynamic model with second order is established and the nonlinear differential dynamic system without constant term is obtained through a transfer process of T=U+b. Hence three fixed points and the homoclinic orbits are found. The critical condition of the chaotic vibration of the elastic arch is given by using the method of Melnikov function. The numerical results of the stationary and chaotic motion are given and discussed.

首先利用拱的单元平衡方程建立了拱的二阶三次非线性动力学模型；然后通过变换使方程转化为不含常数项的非线性微分动力系统，并由此得到无扰动系统的3个不动点与同宿轨道；再用Melnikov函数法给出了发生混沌的临界条件；最后给出了该系统出现定常运动和混沌运动的数值结果。

As an application, it is proved that a continuous map of an interval is chaotic iff it is distributively chaotic in a sequence.

给出紧度量空间上连续映射按序列分布混沌的一个充分条件，并证明区间连续自映射是混沌的当且仅当它是按某序列分布混沌的。

The new transient chaotic neural network algorithm selectively carefully searchs some states to clarify distribution of small and convergence region during chaotic search.

然后根据这些先验信息，更合理地控制暂态神经元的动力学行为。

Firstly, Some of the basic concepts of chaotic vibration are introduced, the qualitative and quantitative methods of chaotic vibration identification are detailed, the selection of associated parameters is studied, the algorithms for calculating the maximum Lyapunov exponent, correlation dimension and periodicity ratio are provided. On the basis of analysis and comparison of different methods, the methods used in the paper are selected.

本文首先介绍了混沌振动的基本概念；评述了混沌振动识别的定性和定量方法；对有关参数的选择进行了研究；给出了计算最大Lyapunov指数、相关维数和周期比的算法；在对不同方法对比分析的基础上，选出了本文拟采用的识别方法。

Warden: That's a beautiful dog, but don't bring her again.

那是条漂亮的狗，但是不要再把她带来了。

You get up in the morning – no hangover!

你第二天早上起来的时候—不会宿醉！