混沌

In this paper,the method of feedback pulse of system variable was applied to control the discrete map and continuous nonlinear system for transforming a stable periodic motion into an unstable chaotic motion.

用系统变量的脉冲反馈法控制离散和连续非线性系统，使系统由稳定的周期运动转变为不稳定的混沌运动。

And the effects of length of data N to the approximate entropy of chaotic system isalso analyzed.All these are accomplished by examining several time series produced by a surperposition of white noise and noise-free data.It uses the discrete system logistic map and continuous system Lorenz attractoras the examples.

以Logistic方程描述的离散系统和Lorenz方程描述的连续系统为例，采用白噪声和无噪声信号以不同的信噪比混迭而成数据的方法，分析了相同数据长度N，不同信噪比下，混沌系统近似熵的变化；相同信噪比，不同数据长度对系统近似熵的影响。

Conley index; prime isolated invariant set; bifurcation point; discontinuity dynamical systems; finite piecewise continuous map; coding; rigorous computer assisted proof; chaos; Ikeda map

基础科学，数学，动力系统理论Conley指标；素孤立不变集；分支点；间断动力系统；有限分片连续映射；编码；计算机严格辅助证明；混沌； Ikeda映射

In the "hard" nonlinear regime, the radiation field is characterized by non-period of the field in time and the continuous power spectrum.

2在"硬"非线性区域，场的混沌振荡态是连续出现的，其特征是输出功率谱是连续谱。

Chaos is a dynamic and species-random and nonlinear system, and it has sensitive initial conditions, continuous power spectrum and traversal, so it is often used to generate pseudo-random sequence.

由于混沌是一种动态的、类随机的非线性系统，且具有对初始条件敏感、连续的功率谱、各态遍历等特性，因此可产生伪随机序列。

In accordance with discrete, non-symmetry and time-delay feedback neural networks, we provide some theoretical criteria to judge the stability for designing the networks. On continuous feedback networks, we built an algorithm to estimate the convergence region. On the HNN feedback networks, an effective optimization algorithm based on the annealing strategy and the chaotic neural network is presented, and some disciplinary conclusions are provided to guide the selection of parameters. Simulation results on benchmark problems demonstrate that the performances of our algorithm are distinctly superior to those of the classic HNN based on gradient descend and stochastic optimization methods based on probabilistic distribution.

针对离散、非对称和时延等三种类型的动态反馈网络，给出了可用于网络设计的稳定性判别准则；针对连续动态反馈网络，建立了其收敛域估计的一个算法；针对以HNN模型描述的动态反馈网络，基于退火策略和混沌神经网络提出了一种高效的优化算法，建立了可用于指导参数选择的一些规律性结论，对典型算例的仿真研究显示，改进算法在各类性能上相对基于梯度下降的传统HNN模型和基于概率分布的随机优化算法，具有明显的优越性。

An application of the quality factor of convex function to chaotic signal analysis was given.

给出了凸函数品质因数在混沌信号分析中的应用实例。

First, the calculation of the correlation dimension of the chaotic analysis method is studied.

首先对混沌分析中的关联维计算方法进行了研究。

Finally, the way of the optical image encryption with chaotic sequence based on joint transform correlator is proposed.

最后，本文提出了利用混沌序列相位对图象在联合变换相关器中进行加解密的方法并作了计算机模拟分析。

Linear deformation of the stator and a Coulomb type of frictional relationship were considered in the model.

分析表明，系统除具有各种形式的周期和概周期振动以外，还具有丰富的混沌运动与分叉现象。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。