共查询到18条相似文献,搜索用时 125 毫秒
1.
进一步研究过焦系统,找到了截断误差诱导阵发混沌的直接实验证据.实验显示,过焦系统的数字解呈现开关阵发混沌的特征,分析解仅是一个简单极限序列;影子效应支配系统演化;截断误差的累计误差是演化轨道的影子距离,影子距离随系统逼近不动点增加,随系统远离不动点减少,增加量与减少量统计上相等;在非双曲不动点的邻域内,存在一个阈值,当累计误差超过该阈值时,影子效应失灵,系统从吸引相跳到排斥相.一种合理的猜测是在非双曲不动点局域截断误差可以诱导出新维度——拓展维.
关键词:
开关阵发混沌
截断误差
过焦系统
拓展维 相似文献
2.
一类不连续不可逆保面积映象可以展示类似耗散的行为,因此可称其为“类耗散系统”.在一种类耗散系统中观察到了椭圆周期轨道及其周围的椭圆岛与映象不连续边界碰撞而消失的现象.周期轨道消失后,经过一系列过渡椭圆周期轨道之后,系统的行为由一个混沌类吸引子主导.在混沌类吸引子刚刚出现时,混沌时间序列呈现层流相与湍流相的无规交替.这一切都与不连续耗散系统中发生的Ⅴ型阵发的相应性质十分相似,因此可称为“类Ⅴ型阵发”.然而,当混沌类吸引子刚刚出现时,仅可以找到最后一个过渡椭圆岛的“遗迹”,并不存在它的“鬼魂”,因此类Ⅴ型阵发不遵从Ⅴ型阵发的特征标度规律.反之,混沌类吸引子的鬼魂却存在于最后一个过渡椭圆周期轨道的类瞬态过程中,因此在类Ⅴ型阵发导致混沌运动的临界点之前,由此“类瞬态混沌奇异集”中逃逸的规律就成为标志这一种临界现象的标度律.这与Ⅴ型阵发又根本不同.
关键词:
类耗散性
类混沌吸引子
类Ⅴ型阵发 相似文献
3.
根据椭圆反射腔物理模型, 提出了一种改变系统演化轨道的切延迟操作方法,导出了基于该方法的一类离散混沌映射系 统.实验表明,这类离散混沌系统最大Lyapunov指数恒大于零,状态变量等概率分布且与参 数和初值无关,全域零相关性,切延迟1单位时存在一个稳定不变的方形吸引子,切延迟大于 1单位时走向各态遍历.这类离散混沌系统可以产生两个独立的伪随机序列,其特殊性质和 复杂的动力学行为极具密码学应用价值.
关键词:
混沌
切延迟
Lyapunov指数
TD-ERCS
吸引子 相似文献
4.
本文使用转移矩阵的方法,引入椭圆角转换函数,使椭圆问题得到简化,推导出十分简单的切延迟椭圆反射的迭代公式,这样非常有利于理论分析.切延迟椭圆反射腔映射系统(TD-ERCS)在切延迟1单位时存在吸引子,利用该公式,对其吸引子形成的原因及稳定性做了理论分析,发现圆的吸引子与椭圆不尽相同;同时发现椭圆有两个不动线,但只有一个是稳定的.本文还发现,随着椭圆压缩因子μ的减小,对于任意的切延迟因子m,相邻两次迭代数据间的相关性增强,这说明将该系统用作密码系统,椭圆压缩因子μ不能太小,同时混沌系统本身要求μ不能太大,否则降低安全度.
关键词:
混沌
切延迟
TD-ERCS
吸引子 相似文献
5.
为了进一步分析切延迟椭圆反射腔映射系统(TD-ERCS)混沌系统的密码学意义上的安全性, 采用TD-ERCS并行方式构造了一个结构简单的伪随机序列发生器.用户密码不再是固定不变的 ,可在[264,2672]区域内任意取值.对所产生的二值伪随机 序列(即TD-ERC S序列)进行了均衡性、游程特性、相关性等基本统计特性初步测试,并与m序列、logistic 序列、Chebyshev混沌序列、SCQC序列作了对比分析.实验表明,TD-ERCS序列有更好的统计 特性.
关键词:
混沌
TD-ERCS
PRNG
统计特性 相似文献
6.
7.
混沌外腔半导体激光器输出明显存在弛豫振荡特征,弛豫振荡频率小于外腔振荡频率时,外腔半导体激光器输出态是短腔机制;反之,外腔半导体激光器输出态是长腔机制.首先对比分析了弛豫振荡频率为5.6 GHz,腔长对频谱有效带宽的影响.然后同时调节注入电流和载流子寿命来大幅度地增加弛豫振荡频率.最后在弛豫振荡频率为40 GHz、腔长为毫米级(4—20 mm)时,实现由短腔机制到长腔机制的转换,进而分析了外腔反馈率和外腔长对外腔半导体激光器频谱带宽的影响.分析结果表明:短腔机制下,输出混沌态不稳定,0.1 mm的偏差就会导致混沌态与非混沌态之间的转化;长腔机制下,输出混沌态稳定,输出混沌区域较大,证明长腔机制下更有益于获得宽带连续的混沌区域.在弛豫振荡频率为40 GHz、外腔长度为毫米级时,实现了外腔半导体激光器的长腔机制,从而增大了高带宽混沌的参数空间. 相似文献
8.
9.
10.
提出了一种基于切延迟椭圆反射腔映射系统(TD-ERCS)的单向Hash函数算法.该算法只需将明文信息线性变换为系统的参数序列,然后让TD-ERCS依次迭代,再依照一定的规则提取Hash值,勿需要增加任何冗余计算.该算法的密钥在[264,2160]内任意取值,输出Hash值长160bit.基础的安全性测试表明,这种Hash函数具有很好的单向性、弱碰撞性、初值敏感性,较其他混沌系统构造的Hash函数具有更强的安全性,且实现简单,运行速度快,是传统Hash函数的一种理想的替代算法.还导出了评估碰撞性的一个客观标准.
关键词:
混沌
Hash函数
TD-ERCS 相似文献
11.
A shell model is introduced to study a turbulence driven by the thermal instability (Rayleigh-Benard convection). This model equation describes cascade and chaos in the strong turbulence with high Rayleigh number. The chaos is numerically studied based on this model. The characteristics of the turbulence are analyzed and compared with those of the Gledzer-Ohkitani-Yamada (GOY) model. Quantities such as a mean value of total fluctuation energy, it's standard deviation, time averaged wave spectrum, probability distribution function, frequency spectrum, the maximum instantaneous Lyapunov exponent, distribution of instantaneous Lyapunov exponents, are evaluated. The dependences of these quantities on the error of numerical integration are also examined. There is not a clear correlation between the numerical accuracy and the accuracy of these quantities, since the interaction between a truncation error and an intrinsic nonlinearity of the system exists. A finding is that the maximum Lyapunov exponent is insensitive to a truncation error. (c) 1999 American Institute of Physics. 相似文献
12.
Vladimir V. Rozanov Alexei I. Lyapustin 《Journal of Quantitative Spectroscopy & Radiative Transfer》2010,111(12-13):1964-1979
Accurate radiance computations with highly peaked phase functions is a challenging problem. The developed truncation methods replace the peak of phase function using different approximations in the cone of forward scattering. The main goal of this paper is to employ a new integral form of similarity conditions to the error analysis of truncation techniques. This analysis emphasizes two main error sources of these methods from (1) truncation of Legendre series, and (2) truncation of the forward cone for peaked phase functions. The first error has an oscillating pattern and is effectively suppressed by the single scattering correction. The second, often overlooked, error manifests itself as a bias which weakly depends on the number of Legendre terms used in the solution unless it becomes comparable to the total order of Legendre expansion series. This paper presents a comparative theoretical and numerical error analysis of the Delta function method [15], Delta-fit method [7], and Delta-M method [21]. The Delta-M method, combined with the single scattering correction, is shown to provide the best overall accuracy for the intensity computations. 相似文献
13.
Bifurcation control and the existence of chaos in a class of
linear impulsive systems are discussed by means of both theoretical
and numerical ways. Chaotic behaviour in the sense of Marotto's
definition is rigorously proven. A linear impulsive controller,
which does not result in any change in one period-1 solution of the
original system, is proposed to control and anti-control chaos. The
numerical results for chaotic attractor, route leading to chaos,
chaos control, and chaos anti-control, which are illustrated with
two examples, are in good agreement with the theoretical analysis. 相似文献
14.
15.
Diffusion in fluids is analyzed at non-classical conditions, intermediate between the Knudsen and Fickian limits. The fluid is considered in the framework of the Einstein’s diffusion evolution equation involving expansions of the density distribution in powers of displacement and time. The standard truncation of these expansions results in the classical model of diffusion; however, higher-order terms lead to a departure from classical behavior. This has not been studied or discussed adequately in the literature previously.Here, we present an exact solution of the Einstein’s diffusion evolution equation without truncation of the density expansions. This solution illustrates limitations in the classical truncations and demonstrates non-classical effects due to large mean free paths, λ. In particular, this new solution shows that, at large λ, there are significant quantitative deviations from classical diffusion profiles. In addition, this solution demonstrates a dramatic change in the diffusion mechanism from the state where the molecular motions are predominantly ballistic to one of molecular chaos. This has implications for fundamentals of fluids between the Knudsen and Fickian limits, and for a variety of fields where evolution of a system includes random, multi-scale displacement of particles, such as nanotechnology, vacuum techniques, turbulence, and astrophysics. 相似文献
16.
Numerical experiments on the efficiency of local grid refinement based on truncation error estimates
Alexandros Syrakos Georgios Efthimiou John G. Bartzis Apostolos Goulas 《Journal of computational physics》2012,231(20):6725-6753
Local grid refinement aims to optimise the relationship between accuracy of the results and number of grid nodes. In the context of the finite volume method no single local refinement criterion has been globally established as optimum for the selection of the control volumes to subdivide, since it is not easy to associate the discretisation error with an easily computable quantity in each control volume. Often the grid refinement criterion is based on an estimate of the truncation error in each control volume, because the truncation error is a natural measure of the discrepancy between the algebraic finite-volume equations and the original differential equations. However, it is not a straightforward task to associate the truncation error with the optimum grid density because of the complexity of the relationship between truncation and discretisation errors. In the present work several criteria based on a truncation error estimate are tested and compared on a regularised lid-driven cavity case at various Reynolds numbers. It is shown that criteria where the truncation error is weighted by the volume of the grid cells perform better than using just the truncation error as the criterion. Also it is observed that the efficiency of local refinement increases with the Reynolds number. The truncation error is estimated by restricting the solution to a coarser grid and applying the coarse grid discrete operator. The complication that high truncation error develops at grid level interfaces is also investigated and several treatments are tested. 相似文献
17.
18.
在包含三能级原子的环形腔的输出光场中,观察到了由电磁感应透明(EIT)效应导致的动态非稳及混沌.该动态非稳及向混沌的过渡可以通过耦合光场而加以很好地控制.同时,由三能级EIT导致的原子相干改变了系统的吸收、色散及非线性效应,从而极大地增强了系统的动态非稳和混沌过渡特性.建立了一个理论模型来定量地解释观察到的现象. 相似文献