混沌系统最重要的性质是初值敏感性和参数敏感性。
A fundamental underlying property in a chaotic system is sensitive dependence on initial conditions and parameters.
给出由传递性产生初值敏感及混沌的几个充分条件。
In this paper, it is introduced that transitivity arise some sufficient condition which sensitive dependence on initial conditions and chaos.
混沌系统的一个重要特性是初值敏感性和参数敏感性。
An important property of chaos system is initial sensitivity and parameter sensitivity.
这些特性包括：不确定性、内在随机性以及初值敏感性。
These characters include: uncertainty, internal stochastic and sensitive to initial conditions.
混沌信号高度的初值敏感性，使得密钥具有非常大的取值空间。
The key space is considerable large because of chaotic signal's high sensitivity to initial values.
利用混沌振子的初值敏感性和对噪声的免疫力可以检测微弱信号。
The weak signal can be detected by chaotic oscillator owing to its property of sensitive dependence on initial conditions and of immunity from noise.
初值敏感性是指混沌系统中初值的微小变化就会导致混沌轨道的很大变化。
Chaos initial value sensitivity refers to small changes of initial value can lead to great changes of chaotic orbit.
初值敏感性是指混沌系统中初值有一微小变化就会引起混沌轨道的很大变化。
Sensitive dependence on initial conditions means that little difference on initial conditions will lead to great changes on chaotic orbit.
混沌系统的参数敏感性和初值敏感性可以用于小信号检测，抑制噪声是其关键。
The parameters sensitivity and initial conditions sensitivity of chaotic systems can be used to detect weak signals, and the noise reduction plays a key role in its realization.
混沌映射因为初值敏感性、参数敏感性、遍历性和类随机性的特点，很适合用于信息加密。
Based on the features of initial value sensitivity, parameter sensitivity, ergodicity and random similarity, chaotic maps are now widely used in information encryption.
基于混沌运动的初值敏感性和对混沌优化搜索过程的分析，提出了并行自适应混沌优化方法。
Based on the initial value sensitivity of chaotic motion and the analysis of optimal searching process, a parallel adaptive chaotic optimization (PACO) method is proposed.
混沌映射所具有的初值敏感性和随机性，使得基于混沌理论的图像加密算法成为一个研究热点。
The initial sensitivity and randomness of the chaotic map make the image encryption algorithm based on chaotic theory become a hot researching field recently.
它具有内禀随机性、初值敏感性和“混沌序”等三个本质特征，蕴涵着一种全新的教育哲学思想。
Inner randomness, Sensitivity to initial value and Chaos order are its intrinsic characteristics. It contains a kind of new educational philosophy.
该算法充分利用混沌的初值敏感性和轨道遍历性，克服了已有混沌变异模型存在搜索盲区大的缺点。
The algorithm makes fully use of initial value sensitivity and track ergodicity of chaos, overcoming the disadvantage of big searching dead zone existed in conventional chaotic mutation model.
利用混合光学双稳混沌序列的伪随机性和初值敏感性，提出一种用于数字水印中的水印图像置乱算法。
Using the sensitivity to the initial conditions and parameters of mixed-optical bistable chaotic sequence, we have a new scrambling algorithm about watermarking image.
由于混沌运动具有初值敏感性和长时间发展趋势的不可预见性，混沌控制就成为混沌应用的关键环节。
Because chaos is characterized by "supersensitivity" to the initial conditions and long term non-forecasts of trajectories, control of chaos is of much importance for the application.
仿真计算结果表明这种离散化的方法应用于此轨道优化问题可以避免传统轨道优化方法对初值敏感的问题。
The results of calculation and simulation indicate that application of the discrete method for problem of trajectory optimization can avoid the problem of initial value sensitivity.
把混沌系统的初值敏感性和易碎水印对篡改的易碎性结合起来，提出一种基于混沌迭代的易碎水印产生方案。
A kind of fragile watermark based on chaotic map is proposed, which combines the initial condition sensitivity of chaotic system with this watermark fragility.
理论分析和模拟试验可以看出，本系统具有较高的初值敏感性、较强的安全性和较好的加密效果，可用于实际的图像加密系统。
After theoretic analysis and simulation experiments, the system has higher sensitivity to initial conditions, better security and encryption effects, so it is adapt for images encryption.
为了解决传统高斯混合模型（GMM）对初值敏感，在实际训练中极易得到局部最优参数的问题，提出了一种采用微粒群算法优化GMM参数的新方法。
The traditional training methods of Gaussian Mixture Model(GMM) are sensitive to the initial model parameters, which often leads to a local optimal parameter in practice.
实验结果表明：动力系统的预报时效不仅与初值误差有关，而且在一定条件下敏感地依赖于计算采用的时间步长和计算精度。
From the result we found that the predictability time is not only depend on initial error but also sensitive to the precision and the time step-size used in the computation.
利用混沌映射具有对初值的敏感性和遍历性等特点，采用多次迭代的一维均衡混沌映射构造了一种非周期、均匀分布的多表代换密码。
Utilize the sensitivity and ergodic characteristic of the chaos map, a non-periodic and uniformity distributing multi-chart substitution is designed with multi-iterative equilibrium chaos map.
利用混沌对初值极端敏感性的特点，能够定位检测对加入水印图像的窜改，并且水印提取不需要原始图像。
The proposed scheme is exploiting the high sensitivity on initial value of chaotic map, can localize the tampers on the watermarked image.
混沌系统的特征是，它们对初值相当敏感。
The trademark of chaotic systems is their sensitivity to initial conditions.
混沌运动的基本特征表现为对初值的敏感依赖性。
An essential feature of chaotic dynamics is sensitively dependent on initial conditions.
混沌系统对初值的敏感性会使系统产生不可预见性和内在随机性，这一特性可以用来隐藏信号，进行混沌通信。
Behavior of the chaos system may be not the foresight, and is the intrinsic randomness for the initial value sensitivity, which can be used to hide signal in the security communication.
混沌序列由于具有很好的伪随机性且具有对初值和参数的敏感性特性，成为处理秘密信息的一个重要的研究方向。
Chaotic sequence has become one of important research direction in treat secret information because of its dummy randomness and sensibility to initial value and parameter.
人工鱼群算法(AFSA)是一种新型的寻优策略，它具有鲁棒性强，全局收敛性好，以及对初值的不敏感性等优点。
Artificial Fish-Swarm Algorithm (AFSA) is a novel optimizing method. It has a strong robustness and good global astringency, and it is also proved to be insensitive to initial values.
结果表明，所提方法具有较大的密钥空间，很好的单向性，初值和密钥敏感性。
The experimental results show that this method has large key space, strong one-way property, and sensitivity to the initial conditions and keys.
结果表明，所提方法具有较大的密钥空间，很好的单向性，初值和密钥敏感性。
The experimental results show that this method has large key space, strong one-way property, and sensitivity to the initial conditions and keys.
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