计算球面对称动力系统Lyapunov指数

通过跟踪球面上相距很近的两个点的球面轨道并计算球面点之间的球内弦长,提出计算球面动力系统轨道的平均Lyapunov指数的计算公式.采用该方法,实现了随机搜索参数并自动计算相应动力系统的Lyapunov指数.当Lyapunov指数大于0时,可得到一个构造球面混沌吸引子的动力系统;当Lyapunov指数小于0时,可得到一个构造球面充满Julia集的动力系统.文中提出的方法可用于随机搜索参数进而生成球面上的对称混沌吸引子和充满Julia集图形.     

迭代函数系IFS吸引子的通用参数控制系统

讨论一个通用的参数控制方法，通过改变参数控制IFS吸引子的形状，最终生成不同的计算机图像。该方法首先给出两个原始三角图形，通过对两者位置和形状的改变得到IFS码，并通过不断引入新的三角形并改变其位置和形状来影响IFS吸引子的外观。最后，给出了利用此参数控制方法进行仿真试验所得到的几个经典IFS吸引子的图形。     

Color Characterization and Balancing by a Nonlinear Line Attractor Network for Image Enhancement

A novel method to map high dynamic range scenes to low dynamic range images utilizing the concept of color characterization, enhancement, and balancing is described in this letter. Each pixel of the image is first characterized by extracting the relationship of the red, green, and blue components along with its corresponding neighbors using a nonlinear line attractor network to form an associative memory. Then, the illumination enhancement process is performed using a hyperbolic tangent function to provide dynamic range compression to each pixel in the image. The slope of the hyperbolic tangent function is controlled using a parameter that is determined by the local and global statistics of the image to facilitate the change of the intensity level. A color balancing process restores the original color characteristics of the image based on learned associative memory matrices which eliminate image distortion due to improper recombination of red, green and blue components after enhancement. Experiments conducted on images captured at extremely uneven lighting environments show that the proposed method outperforms other image enhancement algorithms.     

转子-轴承系统混沌运动的神经网络反馈控制方法

用神经网络技术对刚性Jeffcott转子-轴承系统进行混沌滞延反馈控制研究。研究结果表明,当转子-轴承系统进入混沌状态后,引入时间滞延反馈控制信号,可以消除转子-轴承系统的混沌振动,使嵌入在混沌吸引子中的不稳定周期轨道回到稳定周期轨道上。采用间接误差计算的BP神经网络学习方法和自适应学习率BP算法结合而形成的改进型BP神经网络方法,可以快速搜寻到次优化的滞延反馈控制强度,从而即时有效地消除转子-轴承系统的混沌振动。一旦混沌振动回归稳态周期振动,则反馈控制信号自动消失。该方法为控制转子-轴承系统的振动状态提供了理论依据,特别是对工程实际转子系统有实用价值。     

简化Lorenz系统多翅膀混沌吸引子的设计与电路实现

基于简化Lorenz系统,通过设计非线性函数,得到单方向多翅膀混沌吸引子.在此基础上,通过引入切换控制函数,得到了网格多翅膀混沌吸引子.通过相图、耗散性、平衡点、分岔图和Poincaré截面方法,分析了系统的动力学特性.结果表明,该多翅膀系统具有丰富的动力学行为.设计并实现了网格多翅膀系统的模拟电路,通过示波器观测到网格多翅膀混沌吸引子,验证了该系统的物理可实现性,电路实验结果与数值仿真结果相一致.     

Ergodic Hyperbolic Attractors of Endomorphisms

Let μ be an SRB-measure on an Axiom A attractor Δ of a C ²-endomorphism (M, f). As is known, μ-almost every x ϵ Δ is positively regular and the Lyapunov exponents of (f, T f) at x are constants λ⁽ⁱ⁾(f, μ), 1 ≤ i ≤ s. In this paper, we prove that Lebesgue-almost every x in a small neighborhood of Δ is positively regular and the Lyapunov exponents of (f, T f) at x are the constants λ⁽ⁱ⁾(f, μ), 1 ≤ i ≤ s. This result is then generalized to nonuniformly completely hyperbolic attractors of endomorphisms. The generic property of SRB-measures is also proved. 2000 Mathematics Subject Classification. 37D20, 37D25, 37C40. This work was supported by the 973 Funds of China for Nonlinear Science, the NSFC 10271008, and the Doctoral Program Foundation of the Ministry of Education.     

五平衡点非线性系统的多核混沌运动分析

研究了外力矩作用下刚体转动动力学系统存在的混沌吸引子类型、数量和特性,分析了5个平衡点的属性。系统状态在5个平衡点邻域沿某方向的收敛和沿某方向的发散,可以形成各种各样的周期吸引子,单核、双核、三核、连体四核、单体四核混沌吸引子。该系统中包含的各类混沌运动形式复杂,吸引子种类繁多。     

三维矩形布局吸引子性质的研究

吸引子法作为一种量化的定位规则,在解决三维布局问题时取得了较好的效果。 对解决三维矩形布局问题的吸引子法进行了研究,获得了吸引子法的一些基本性质,如最佳布 入点、吸引子法的趋角性、隐性吸引子的“唯一”性以及位置的“动态性”等,有利于吸引子法在 三维矩形布局求解中得到更好地运用。     

油水两相流流型混沌吸引子形态特性

基于在垂直上升管中采集到的61组油水两相流电导波动信号,通过在混沌吸引子域中放置参考截面方法,考察了混沌吸引子形态特征量与油水两相流流型转变之间的关系,发现水包油流型在3阶及4阶吸引子矩特征量平面上分布相对稳定,而过渡流型在3阶吸引子矩特征量平面上呈不规则剧烈变化,在4阶吸引子矩特征量平面上呈线性变化。研究结果表明,油水两相流混沌吸引子形态特征量对流型转化敏感,有助于理解油水两相流流型转化的非线性动力学机制。     

Towards monitoring electrostatics in gas–solid fluidized beds

The electrostatic charge distribution in a lab‐scale 2‐D fluidized bed of 900 µm glass beads was determined using arrays of induction probes, and the influence of relative humidity and superficial gas velocity was examined. The bubble presence, relative humidity, and superficial gas velocity were found to influence charge separation. Bipolar charging was observed; the net charge build‐up was found to be negligible. Moreover, the system was monitored by applying the attractor comparison method to the electrostatic charge signals from an induction probe. It was concluded that this approach can indeed be used to monitor changes in the electrostatic behaviour.