共查询到19条相似文献,搜索用时 78 毫秒
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研究了空间单位区域内两个曲面映射构成的动力系统的混沌特性.研究发现两个曲面中有一个曲面振荡剧烈,另外一个曲面随机生成时系统更容易出现混沌,能生成众多有特点的混沌吸引子.如果调整随机曲面使其成为满射,那么所构成的动力系统是混沌的概率可以达到1/2或者更高.通过计算Lyapunov指数以及绘制分岔图等方法对系统的混沌特性进行分析,同时给出了由两个曲面构造的系统出现混沌的必要条件.和二维情形一样,一个三维正弦函数与两个三维多项式函数构造的动力系统是混沌的概率也很高,通过计算可以得到众多的具有观赏和实用价值的三维吸引子. 相似文献
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研究平面单位区域内的二次函数的混沌特性,发现标准二次跌射是Li-Yorke混沌的,也是Devaney混沌的;在满足一定条件下,还存在大量的二次函数是混沌的.一些二次函数可以使用平移与缩放等变换化为标准二次函数,其混沌特性不变;同时,对单位区域上的非标准二次函数进行了初步的研究.通过计算Lyapunov指数以及绘制分岔图等对二次曲线的混沌特性进一步分析,其中参数变化的分岔图以及混沌曲线控制点的区域分布图等有一定的研究价值.另外研究表明,使用多个二次曲线交叉迭代能够产生较好的混沌序列,该混沌序列可以应用于图像加密等一些实际应用领域. 相似文献
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实验利用双反馈半导体激光器获得了关联维数为3.8的高维混沌光.同时对比分析了双反馈与单反馈两种不同模式产生混沌的区别.结果表明:在反馈强度均为-26 dB时,双反馈产生混沌的关联维数高于单反馈产生混沌的关联维数2.6;双反馈可获得带宽为11 GHz的混沌光,为单反馈产生混沌带宽5.5 GHz的两倍.当双反馈的两个外腔长度不相等时,混沌的自相关曲线能很好的隐藏外腔长度信息,可提高混沌通信的保密性.
关键词:
双反馈
半导体激光器
混沌
带宽 相似文献
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针对图像水印在不可见性和鲁棒性方面很难同时满足的问题。提出一种基于混沌对原始水印图像进行双重加密的方法,使水印信息具有双重的保密性;根据人眼视觉系统将不同强度的水印分量自适应地嵌入到DCT的中频系数中,使嵌有水印的图像具有良好的视觉不可见性。实验表明,该算法在水印自身的安全性和相关性,系统的鲁棒性方面相对于其它算法都有很大的提高。 相似文献
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提出了一种用于图像加密的可逆二维混沌映射,该映射由左映射和右映射两个子映射组成。通过对图像的拉伸和折叠处理,实现了图像的混沌加密。首先沿图像的对角线方向将正方形图分为上下两个部分并重新组合成一个平行四边形的图像;然后利用平行四边形图像的两列像素之间的像素数目差将某列中的像素插入到相邻下一列像素之间。经过这样的过程,原始图像拉伸成为一条直线。最后按照原始图像的大小将这条直线折叠成为一个新的图像。推导出了映射的数学表达式,设计了密钥产生的方法,分析了图像加密算法的安全性问题。仿真验证了该图像加密算法的有效性。 相似文献
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为了产生复杂的混沌吸引子,构造了一个新的三维二次自治混沌系统.该系统含有三个参数,每一个方程含有一个非线性乘积项.利用理论推导、数值仿真、Lyapunov指数谱和分岔图对系统的基本动力学特性进行了分析.结果表明,该系统具有五个平衡点,因而与Lorenz,Rsslor,Chen、Lü等混沌系统是非拓扑等价的;当其参数满足一定条件时,系统是混沌的.与Lorenz等混沌系统相比,该系统具有更大的正Lyapunov指数,能够产生复杂的混沌吸引子和一些有趣的动力学行为.最后,设计了实现该系统的混沌电路,电路实验结
关键词:
三维二次自治系统
混沌
混沌吸引子
电路实现 相似文献
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初值敏感性是混沌的本质,混沌的随机性来源于其对初始条件的高度敏感性,而Lyapunov指数又是这种初值敏感性的一种度量.本文的研究发现,混沌系统的级联可明显提高级联混沌的Lyapunov指数,改善其动力学特性.因此,本文研究了混沌系统的级联和级联混沌对动力学特性的影响,提出了混沌系统级联的定义及条件,从理论上证明了级联混沌的Lyapunov指数为各个级联子系统Lyapunov指数之和;适当的级联可增加系统参数、扩展混沌映射和满映射的参数区间,由此可提高混沌映射的初值敏感性和混沌伪随机序列的安全性.以Logistic映射、Cubic映射和Tent映射为例,研究了Logistic-Logistic级联、Logistic-Cubic级联和Logistic-Tent级联的动力学特性,验证了级联混沌动力学性能的改善.级联混沌可作为伪随机数发生器的随机信号源,用以产生初值敏感性更高、安全性更好的伪随机序列. 相似文献
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Chaos game representation of functional protein sequences, and simulation and multifractal analysis of induced measures 下载免费PDF全文
Investigating the biological function of proteins is a key
aspect of protein studies. Bioinformatic methods become important
for studying the biological function of proteins. In this paper, we
first give the chaos game representation (CGR) of randomly-linked
functional protein sequences, then propose the use of the recurrent
iterated function systems (RIFS) in fractal theory to simulate the
measure based on their chaos game representations. This method helps
to extract some features of functional protein sequences, and
furthermore the biological functions of these proteins. Then
multifractal analysis of the measures based on the CGRs of
randomly-linked functional protein sequences are performed. We find
that the CGRs have clear fractal patterns. The numerical results
show that the RIFS can simulate the measure based on the CGR very
well. The relative standard error and the estimated probability
matrix in the RIFS do not depend on the order to link the functional
protein sequences. The estimated probability matrices in the RIFS
with different biological functions are evidently different. Hence
the estimated probability matrices in the RIFS can be used to
characterise the difference among linked functional protein
sequences with different biological functions. From the values of
the D_q curves, one sees that these
functional protein sequences are not completely random.
The D_q of all linked functional proteins studied are
multifractal-like and sufficiently smooth for the C_q (analogous
to specific heat) curves to be meaningful. Furthermore, the D_q
curves of the measure \mu based on their CGRs for different orders
to link the functional protein sequences are almost identical if
q\geq 0. Finally, the C_q curves of all linked functional
proteins resemble a classical phase transition at a critical point. 相似文献
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HAO Jian-Hong XU Hai-Bo YU Jin-Jiang 《理论物理通讯》2007,48(2):79-287
We demonstrate the constant feedback and the modified constant feedback method to the Hénon map. Using the convergence of the chaotic orbit in finite time, we can control the system from chaos to the stable fixed point, and even to the stable period-2 orbit or higher periodic orbit by the action of a proper feedback strength and pulse interval. We also find that the multi-steady solutions appear with the same control strength and different initial conditions. The aim of this control method is explicit and the feedback strength is easy to determine. The method is robust under the presence of weak external noise. 相似文献
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对偶极玻色-爱因斯坦凝聚体(Bose-Einstein condensate,BEC)在类方势阱中的Bénard-von Kármán涡街现象进行了数值研究.结果表明,当障碍势在BEC中的运动速度与尺寸在适当范围内时,系统中会出现稳定的两列涡旋对阵列,即Bénard-von Kármán涡街.研究了偶极相互作用强弱、障碍势尺寸以及运动速度对尾流中产生的涡旋结构的影响,得到了相图结构.对障碍势所受拖拽力进行计算,分析了涡旋对产生的力学机理. 相似文献
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采用Chin和Chen的动力学算法追踪粒子在体系中的运动情况, 首次研究并对比了粒子在Hénon-Heiles体系与变形Hénon-Heiles六边形体系中的混沌逃逸规律, 在Hénon-Heiles体系中, 对于不同能量范围, 分形维数与逃逸率随能量而改变, 但在变形Hénon-Heiles六边形体系中, 仅在低能区分形维数与逃逸率随能量的改变而变化, 而高能区逃逸率和分形维数趋于稳定值. 并且得到普遍规律, 即不同混沌体系中粒子的混沌逃逸率和粒子逃逸的分形维数呈现较强的线性相关性. 因而分形维数可以作为工具研究混沌体系中粒子的逃逸规律, 在介观器件设计中可以通过研究混沌电子器件的分形维数来表征粒子在器件中的传输行为. 相似文献
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Kei Inoue 《Entropy (Basel, Switzerland)》2022,24(6)
The Lyapunov exponent is the most-well-known measure for quantifying chaos in a dynamical system. However, its computation for any time series without information regarding a dynamical system is challenging because the Jacobian matrix of the map generating the dynamical system is required. The entropic chaos degree measures the chaos of a dynamical system as an information quantity in the framework of Information Dynamics and can be directly computed for any time series even if the dynamical system is unknown. A recent study introduced the extended entropic chaos degree, which attained the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. Moreover, an improved calculation formula for the extended entropic chaos degree was recently proposed to obtain appropriate numerical computation results for multidimensional chaotic maps. This study shows that all Lyapunov exponents of a chaotic map can be estimated to calculate the extended entropic chaos degree and proposes a computational algorithm for the extended entropic chaos degree; furthermore, this computational algorithm was applied to one and two-dimensional chaotic maps. The results indicate that the extended entropic chaos degree may be a viable alternative to the Lyapunov exponent for both one and two-dimensional chaotic dynamics. 相似文献
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Synchronization of spatiotemporal distributed system is investigated by considering the model of 1D dif-fusively coupled complex Ginzburg-Landau oscillators. An itinerant approach is suggested to randomly move turbulentsignal injections in the space of spatiotemporal chaos. Our numerical simulations show that perfect turbulence synchro-nization can be achieved with properly selected itinerant time and coupling intensity. 相似文献
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Application of Chaos in Genetic Algorithms 总被引:2,自引:0,他引:2
Through replacing Gaussian mutation operator in real-coded genetic algorithm with a chaotic mapping, wepresent a genetic algorithm with chaotic mutation. To examine this new algorithm, we applied our algorithm to functionoptimization problems and obtained good results. Furthermore the orbital points‘ distribution of chaotic mapping andthe effects of chaotic mutation with different parameters were studied in order to make the chaotic mutation mechanismbe utilized efficiently. 相似文献
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The models of rf-driven Josephson junctions are investigated as the perturbed systems.It is shown that the heteroclinic orbits corrected by perturbations are stable if some relations between the initial constants and system parameters are satisfied, which leads to Melnikov chaos. To stabilize chaos one has to make the control parameters fitting the relations.The result is compared with the previous numerical work and a good agreement is found. 相似文献