液晶混合光学双稳装置中分叉和混沌行为

本文报道在t_R>>τ(t_R为反馈系统延迟时间,τ为液晶的弛豫时间)条件下,液晶混合光学双稳装置中,随着系统参数的改变,自脉冲经倍周期分叉发展到混沌的过程。计算了分叉图,通过频谱和相空间图能清晰地分析系统的动态行为。实验结果与Ikeda理论进行了比较。 关键词：     

液晶混合光学双稳装置中的分叉、混沌和暂态行为

本文以时延弛豫微分方程为出发点,计算和分析了具有反馈时间延迟(feedbacktime-delay)t_R的液晶混合光学双稳系统中的分叉和混沌。还发现在双稳区内存在一种周期为t_R的暂态振荡。 关键词：     

光学双稳态和混沌运动中的临界现象

本文以具有反馈时间延迟的非线性系统弛豫方程为出发点,讨论了双稳态临界点的临界现象。发现双稳区边沿的临界慢化与混沌运动中切分叉点附近阵发混沌时间间隔发散具有一致性,临界指数为1/2。在双稳区(尖顶突变模型)的尖顶处,与双稳区边沿临界点不同,它与混沌运动中倍周期分叉点及劈分叉点的临界慢化具有一致性,临界指数为1。上述结果具有普适性。以液晶混合光学双稳系统为例,进行了计算机实验,其结果与分析相一致。 关键词：     

反铁电液晶TFMHxPOCBC-D2中CD2偏振红外光谱及手性烷基链受阻转动的研究

观测到反铁电液晶分子TFMHxPOCBC-D₂(4-(trifluoromethylhexy-3-d₂ carbonyl)phenyl 4'-octyloxybiphenyl caboxylate) 中CD₂的偏振红外光谱中液晶分子的手性烷基链的受阻转动，以及较大的双色吸收特性.应用一个分子模型，进行了偏振红外吸收的模拟计算，与实验结果相比较，得到液晶分子手性烷基链与分子长轴的夹角约为70°, 其受阻方向在液晶分子倾斜方向一侧的半圆内. 关键词：     

低压驱动液晶透镜设计的研究

探讨了低压液晶透镜设计的规律. 由五种液晶材料的Δn_eff随驱动电压变化的规律可知: 如果液晶材料归一化Δn_eff控制在 95%以下, 驱动电压可控制在10 V以下; 在能满足透镜性能和制备工艺允许的前提下, 设计液晶透镜时选取的归一化Δn_eff越小, 获得的液晶透镜驱动电压越低. 该规律可为高性能液晶透镜的设计与制备提供指导. 关键词： 液晶透镜 设计 低压驱动 n_eff')" href="#">归一化Δn_eff     

沟道效应的运动阻尼与系统走向混沌的临界特征

利用正弦平方势,把粒子运动方程化为具有运动阻尼和周期调制的摆方程.利用Melnikov方法分析了系统的全局分叉和混沌行为，指出了沟道辐射本底增强和沟道效应的无规行为与混沌之间的相关性. 关键词： 沟道效应 摆方程 分叉 混沌     

用X射线散射法研究HF,HCI,H2SO4和HAC对磷脂酰乙醇胺液晶结构影响的机理

采用小角X射线散射法(SAXS)研究了HF,HCl,H₂SO₄和HAC分别对含水磷脂酰乙醇胺(PE)液晶结构的影响。通过研究发现,HF有使PE液晶态变成C相的机理,HCl有使PE液晶态变成LH相的机理,H₂SO₄有使PE液晶态变成L_a相的机理。而HAC则有使PE液晶态经过L_a相转变成LH相的机理。 关键词：     

双光反馈半导体激光混沌系统中外腔延时反馈特征的抑制

在一个双光反馈半导体激光混沌系统中,固定其中一个反馈腔镜(固定腔M₁)的反馈延迟时间以及反馈强度,实验研究了另一个反馈腔镜(可变腔M₂)的反馈延迟时间以及反馈强度对系统混沌输出的延时反馈特征的影响.研究结果表明:在可变腔M₂与固定腔M₁的反馈强度相等的条件下,改变M₂的腔长,当其腔长约等于(但不能严格等于)M₁的腔长或者腔长的一半时,系统将呈现较好地抑制延时反馈特征效果;当M 关键词： 半导体激光器 双光反馈 混沌输出 延时特征     

一维 Frenkel-Kontorova(FK)模型原子链的相变研究

文章基于一维Frenkel-Kontorova模型,研究了边界原子的初始速度对原子链运动状态的影响,数值模拟结果表明:当v1时,原子处于"振荡区",当v₁2时,原子处于"混沌区",当v>v₂时,原子处于 "均匀区". 同时我们发现临界速度v₁和v₂随原子数目和垫底势高度的变化而变化. 关键词： Frenkel-Kontorova(FK)模型 相变     

谐和与噪声联合作用下Duffing振子的安全盆分叉与混沌

研究了软弹簧Duffing振子在确定性谐和外力和有界随机噪声联合作用下，系统安全盆的侵蚀和混沌现象.推导出系统的随机Melnikov过程，根据Melnikov过程在均方意义上出现简单零点的条件给出了系统出现混沌的临界值，然后用数值模拟方法计算了系统的安全盆分叉点.结果表明，由于随机扰动的影响，系统的安全盆分叉点发生了偏移，并且使得混沌容易发生. 关键词： Duffing振子 安全盆 分叉 混沌     

一种新的三维自治混沌系统

通过对蔡氏电路的研究,提出了一种新的混沌系统,并对该系统的基本动力学特性进行了深入研究,得到该系统的Lyapunov指数和Lyapunov维数,给出了相图、Lyapunov指数谱、分岔图、Poincaré映射以及功率谱等.利用OrCAD-PSpice软件设计了该新混沌系统的振荡电路并进行了仿真实验.研究结果表明,该系统与蔡氏电路产生的混沌吸引子并不拓扑等价,且该系统的参数变化范围较大,最大Lyapunov指数接近1,数值仿真和电路系统实验仿真具有很好的一致性,证实了该系统的存在性和物理上可实现性. 关键词： 混沌系统 Lyapunov指数谱 分岔图 电路实现     

A delayed modified Ricker map and its cicada-type oscillations

Without trying to develop a model for a biological system, we introduce a delay map that shows a large spike followed by 16 iterations of much smaller values. Upon variation of one of the parameters, we can get a 13 cycles stable oscillation. The analyses of the bifurcation diagrams for the delayed extended Ricker's map yield a straightforward approach to find parameter values for any periodicity. In particular, we determine the values for the 13 and 17 periodic oscillations. We also notice that the bifurcation diagrams show no chaotic regions, and their structures show self-similarity properties. In general, the bifurcation diagrams have self-similarity structures, where n-periodic oscillations change into (n-1)-periodic oscillations.     

Logistic映射分岔图局部放大的计算机模拟

本文介绍了一种实现Logistic映射分岔图局部放大的计算机模拟方法，对Logistic映射分岔图上任意局部范围可实现10。以上的放大，便于观察Logistic映射分岔图混沌区内的精细结构，该方法实现的计算机模拟过程响应速度快，可实时产生Logistic模型分岔图局部放大的计算机模拟图像，适合于课堂教学计算机模拟实时演示．     

分数阶混沌系统的Adomian分解法求解及其复杂性分析

根据分数阶微分定义,采用Adomian分解算法,研究了分数阶简化Lorenz系统的数值解.研究发现,该算法与预估-校正算法相比,求解结果更准确,所耗计算资源和内存资源更少,求解整数阶系统时较Runge-Kutta算法更准确;利用Adomian算法得到的分数阶简化Lorenz系统出现混沌的最小阶数为1.35,比利用预估-校正算法得到的最小阶2.79更小.采用相图、分岔图分析了该系统的动力学特性,基于谱熵算法(SE)和C0算法分析了该系统的复杂度.结果表明,复杂度结果和分岔图一致,说明系统的复杂度同样能反映出系统动力学特性;复杂度随阶数q的增加呈总体减小的趋势,而混沌态时系统参数c变化对系统复杂度影响不大.为分数阶混沌系统应用于信息加密、保密通信领域提供了理论与实验依据.     

Theoretical and experimental study of discrete behavior of Shilnikov chaos in a CO 2 laser

The discrete distribution of homoclinic orbits has been investigated numerically and experimentally in a CO₂ laser with feedback. The narrow chaotic ranges appear consequently when a laser parameter (bias voltage or feedback gain) changes exponentially. Up to six consecutive chaotic windows have been observed in the numerical simulation as well as in the experiments. Every subsequent increase in the number of loops in the upward spiral around the saddle focus is accompanied by the appearance of the corresponding chaotic window. The discrete character of homoclinic chaos is also demonstrated through bifurcation diagrams, eigenvalues of the fixed point, return maps, and return times of the return maps. Received 28 September 2000 and 27 October 2000     

Effect of metal oxide arrester on the chaotic oscillations in the voltage transformer with nonlinear core loss model using chaos theory

In this paper, controlling chaos when chaotic ferroresonant oscillations occur in a voltage transformer with nonlinear core loss model is performed. The effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of voltage transformers is studied. The metal oxide arrester(MOA) is found to be effective in reducing ferroresonance chaotic oscillations. Also the multiple scales method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes sub-harmonic, quasi-periodic, and also chaotic oscillations. In this paper, the chaotic behavior and various ferroresonant oscillation modes of the voltage transformer is studied. This phenomenon consists of different types of bifurcations such as period doubling bifurcation(PDB), saddle node bifurcation(SNB), Hopf bifurcation(HB), and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are illustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via the multiple scales method to obtain Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system.     

Dynamics of a neuron model in different two-dimensional parameter-spaces

We report some two-dimensional parameter-space diagrams numerically obtained for the multi-parameter Hindmarsh-Rose neuron model. Several different parameter planes are considered, and we show that regardless of the combination of parameters, a typical scenario is preserved: for all choice of two parameters, the parameter-space presents a comb-shaped chaotic region immersed in a large periodic region. We also show that exist regions close these chaotic region, separated by the comb teeth, organized themselves in period-adding bifurcation cascades.     

Performance characteristics of positive and negative delayed feedback on chaotic dynamics of directly modulated InGaAsP semiconductor lasers

The chaotic dynamics of directly modulated semiconductor lasers with delayed optoelectronic feedback is studied numerically. The effects of positive and negative delayed optoelectronic feedback in producing chaotic outputs from such lasers with nonlinear gain reduction in its optimum value range is investigated using bifurcation diagrams. The results are confirmed by calculating the Lyapunov exponents. A negative delayed optoelectronic feedback configuration is found to be more effective in inducing chaotic dynamics to such systems with nonlinear gain reduction factor in the practical value range.      

一个新混沌系统及其电路仿真

提出了一个新的三维自治混沌系统,并对系统的基本动力学特性进行了深入研究, 得到系统的Lyapunov指数和维数,给出了系统数值仿真图、Poincaré 映射图、Lyapunov指数谱和分岔图, 重点分析了不同参数变化对系统动力学行为的影响.最后,设计了该混沌系统的硬件电路并运用Multisim软件 对该电路进行仿真实现,数值仿真和电路仿真证实了该混沌系统与以往发现的混沌系统并不拓朴等价, 是一个新的混沌系统.     

Lyapunov exponent diagrams of a 4-dimensional Chua system

We report numerical results on the existence of periodic structures embedded in chaotic and hyperchaotic regions on the Lyapunov exponent diagrams of a 4-dimensional Chua system. The model was obtained from the 3-dimensional Chua system by the introduction of a feedback controller. Both the largest and the second largest Lyapunov exponents were considered in our colorful Lyapunov exponent diagrams, and allowed us to characterize periodic structures and regions of chaos and hyperchaos. The shrimp-shaped periodic structures appear to be malformed on some of Lyapunov exponent diagrams, and they present two different bifurcation scenarios to chaos when passing the boundaries of itself, namely via period-doubling and crisis. Hyperchaos-chaos transition can also be observed on the Lyapunov exponent diagrams for the second largest exponent.