Chaos from a buck switching regulator operating in discontinuous mode

A first-order iterative map which describes the dynamics of a simple feedback buck switching regulator operating in discontinuous mode is derived. Analysis of this map shows that flip bifurcations occur at certain values of the feedback factor. Results from computer simulations and experiments reveal that the system exhibits a typical perioddoubling route to chaos under the particular operating condition studied in this paper. It is found that a special kind of randomness, arising from the ability of the system to ‘merge’ and ‘skip’ periods, constitutes a unique feature of the chaotic dynamics of switched-mode converter circuits.     

电力负荷记录时间序列混沌特性研究的几点注记

已经发现某些电力负荷记录具有混沌特性，而另外一些却不具有。电力负荷记录具有明显的随机成因，这就提出了“从随机性到混沌”的途径问题。需要根据实际问题研究的需要，放弃“混沌一定来自确定性非线性系统”的现有概念。这对于加深理解“确定性、混沌、随机性”之间的关系有一定的启发。     

Generation of pseudo‐random numbers by chaos‐type function and its application to cryptosystems

The logistic map is known to be one of the nonlinear difference equations as a chaos map, and to generate pseudo‐random numbers. However, since the chaos has a highly sensitive dependence on initial conditions and accumulates inevitable round‐off errors caused by iterating the map, the numerical generation of exact chaotic time series is said to be impossible. The aim of this paper is, first, to propose an algorithm to generate exact chaotic time series of a chaos‐type function derived from the exact chaos solution. Next, the pseudo‐random numbers are evaluated by four tests and the accumulation of chi‐square values. Also, an application to cryptosystems, which do not need the synchronization in usual computer environments, is considered. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 163(2): 67–74, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20436     

基于一维Lozi混沌映射的PFM技术研究

混沌频率调制由于其良好的宽频特性已在脉冲频率调制(PFM)技术中占有重要地位,在此通过对加入混沌调制前后的方波脉冲进行傅里叶分析,对比得出了混沌频率调制的原理,并讨论了一维Lozi混沌映射序列的分布特性.在此基础上,构建了基于脉冲频率调制的逆变器试验平台,采用一维Lozi混沌映射进行了PFM实验.对该混沌映射下的最大幅...     

电流控制模式下Boost变换器的混沌行为

该文建立了Boost变换器在电流可编程控制模式下的离散数学模型和迭代方程，并通过仿真分析了不同分岔参数变化下的工作规律，证实了该变换器中的倍周期和混沌行为。     

负荷预报的混沌时间序列分析方法

某些非线性确定性系统表现出混沌行为,由这些系统产生的时间序列又表现出随机性,但是,这些混沌时间序列在短期内可有较为精确的预测,可以为其建立确定性的预测模型。为了探讨负荷时间序列中的混沌特性,作首先介绍计算时间序列中的多种混沌征数的方法,在发现华中电网发电负荷时间序列中的混沌特性的基础上,给出一种基于混沌理论的局部预测算法。该预测方法的优点是,如果时间序列比较长,就可以通过某些参数的调整来控制预测精度。最后以华中电网的发电负荷为例检验了本中的算法,最终的预测模型的预测效果良好。     

Banded chaos in power systems

This paper focuses on one aspect of ferroresonance in power systems, i.e., the appearance of a strange attractor with a band-like structure. This attractor was called a “pseudoperiodic” attractor in a previous paper where the phenomenon was first reported. It was found in this study that banded chaos arises from a sequence of period doubling bifurcations. Odd-subharmonics undergo a symmetry-breaking bifurcation before the period doubling cascade takes place. A theoretical discussion of symmetry-breaking and period doubling is given and a route to banded chaos in an actual power system is demonstrated. The Lyapunov exponents for the strange attractor were calculated     

Numerical modeling of the route‐to‐chaos of semiconductor lasers under optical feedback and its dependence on the external‐cavity length

This paper investigates numerically influence of the external‐cavity length on the type of the route‐to‐chaos of semiconductor lasers under external optical feedback. The study is based on numerical solution of a time‐delay model of rate equations, and the solutions are employed to construct bifurcation diagrams and to examine the Fourier frequency spectrum of the laser output. The ratio of the relaxation frequency to the external‐cavity resonance frequency is employed to measure the influence of the length of the external cavity. The route‐to‐chaos is period doubling when this frequency ratio is less than unity. The route is sub‐harmonic when the frequency ratio increases up to 2.25. When the frequency ratio increases further, the transition to chaos becomes quasi‐periodic characterized by the compound‐cavity frequency and the relaxation frequency as well as their difference. Copyright © 2009 John Wiley & Sons, Ltd.     

微扰电力系统中的次谐及混沌轨道

研究了电力系统在周期和准周期扰动下的次谐和混沌轨道。首先假定扰动具有正统形式，采用梅尼科夫方法对其中存在的次谐轨道和混沌吸引子进行了系统的分析，指出了连续的次谐分叉进入混沌状态的途径。对周期非正统扰动情况的分析表明，该状态下的系统动力学性质与正统周期扰动情况下类拟，但轨道空间形式更为复杂。对于准周期扰动情况，首先给出了不变环面的存在条件，然后预见了弱扰动下混沌轨道附近的混沌环面及强扰动下环面破裂所产生的混沌现象，并通过数值仿真对其进行了验证。     

安康水电站近坝库岸任家山滑坡性态分析

本文对任家山滑坡的监测资料进行了分析 ,结合实地考察 ,认为滑坡已出现剪破迹象。该滑坡体一旦快速滑入水库将威胁大坝安全 ,建议对其做相应的工程处理并保证正常监测。     

行波超声波电动机混沌建模与分析

作为一个复杂的非线性动力学系统,在一定的参数范围和外部输入条件下,行波超声波电动机系统存在复杂的混沌运动,但至今未见相关研究。在建立行波超声波电动机非线性混沌分析模型基础上,分析行波超声波电动机转速控制系统的Lyapunov指数谱、分岔图及电压相对于转速的轨迹图等非线性运行特性,为超声波电动机的混沌控制及反控制研究奠定了基础。     

电流模式Boost变换器中切分岔迭代映射构造

切分岔是非线性动力系统中的一种特殊分岔,本文研究了因切分岔而引发的变换器电路的阵发混沌现象.首先建立了符合实际电路限定条件下的离散迭代映射模型,然后通过数值仿真手段构造了阵发混沌中主要的周期3、周期4、周期5及平行周期3等周期窗的切分岔离散迭代映射,从而阐述了开关DC-DC变换器电路发生阵发混沌的机理和各周期窗形成的原因.     

基于频闪映射的Boost PFC变换器中的间歇性分岔和混沌现象分析

该文推导出了一组频闪映射方程来精确描述峰值电流控制型Boost PFC变换器的非线性动力学特性。数值模拟发现了系统电流在输入电压周期内会出现间歇性分岔和混沌现象，并对这种间歇性分岔和混沌的周期性进行了分析。通过对系统占空比的详细研究，发现系统并没有经过倍周期分岔的充分发展到达混沌，而是在倍周期分岔的过程中，发生边界碰撞分岔后以非光滑的方式直接进入混沌的。最后，给出了在输入电压幅值、参考电压和负载变化下系统的稳定域。这些结果对实际电路的设计具有重要的参考价值。     

Josephson结电路系统的混沌控制

本文在考虑隧道效应的前提下,分析了含Josephson结电路系统的复杂非线性动力学,建立了系统的非线性动力学方程。根据系统的相图、分叉图及Lyapunov指数图分析了系统由周期运动进入混沌运动的过程。利用外加耦合控制器和利用非线性状态反馈反馈法两种方法实NT系统混沌运动的周期控制,得到了受控系统的周期运动相图及混沌控制控制参数变化时的分叉图。并讨论了这两种控制方法的特点。     

基于混沌时间序列的大型风电场发电功率预测建模与研究

通过对风力发电系统的发电功率时间序列进行低维非线性动力学建模,表明该时间序列呈现混沌特性。在此基础上,利用混沌时间序列的相空间理论建立了风力发电功率神经网络预测模型,对风力发电功率的短期预测进行了分析和研究,并得到了较高的精度。本文研究数据均来自大唐赛罕坝百万千瓦级风电场。     

基于混沌优化支持向量机的火电厂NO_x排放量预测

在传统支持向量机的基础上,建立了基于混沌优化算法优化的支持向量机预测模型,提高了支持向量机的预测精度。根据1995~2009年的NOx统计数据,对2010年的NOx排放量进行了预测,验证了预测模型的合理性。     

周期参数扰动电力系统中的倍周期分叉、混沌和奇怪吸引子

本文在建立一般周期参数扰动下电力系统模型基础上，首次用数值方法发现了电力系统经倍周期分叉通向混沌的道路，并捕捉到了奇怪吸引子，用频谱分析和Ｐｏｉｎｃａｒｅ映射确认了奇怪吸引子的存在。本文的研究表明，电力系统确实存在着混沌振荡。这给电力系统稳定问题的研究提出了新的课题。     

并联降压变换器的非线性行为分析与控制

以主从控制的并联降压型变换器为研究对象,通过实验得到间歇混沌等非线性行为,并通过特征值分析法进行验证,揭示了开关变换器工作中不规则运动产生的原因,为电路设计提供理论依据;在此基础上,提出时间与参数映射的方法和混沌控制的解决方案——相移法。通过将系统的其中一个驱动控制信号发生相位移动或延迟,把系统的混沌运动状态转变为规则运动状态,从而实现了并联降压型变换器电路的混沌控制。相移前后功率谱的变化充分说明了相移法实现混沌控制的可行性和正确性。     

一种基于帐篷映射的混沌搜索全局最优方法

利用混沌的随机性、遍历性和规律性进行优化计算，搜索全局最优，可以避免系统落入局部最优陷阱。本文将具有均匀分布函数的帐篷映射引入到混沌优化算法中，并与共轭梯度法相结合，比Logistic混沌映射确定的算法能更快、更有效地搜索到全局最优解。仿真表明该算法是有效的。     

Lyapunov exponent and bifurcation characteristics in synchronous machines with an internal fault

In this paper, first, turn‐to‐turn fault in a synchronous machine stator winding is investigated, and its inductances are derived with the winding function method. Then, using the nonlinear control theory, the first‐order Poincaré map of the synchronous machine is computed, and a new extended Poincaré map of the machine is established. Also, the characteristic multipliers of the synchronous machine are calculated by the Poincaré map. This new map is capable of analyzing electrical machines in the nonlinear and unbalanced cases for evaluation of stability, bifurcation, and chaos phenomena. The results show that the new map is an effective technique for modeling and analyzing any AC electrical machines. The characteristic multipliers and the Lyapunov exponents of the extended map indicate the system's condition. Chaotic phenomena are observed in some machines with internal faults. Since chaotic systems have a continuous spectrum and various kinds of frequencies in their spectrum, identification of the internal fault location is not easy with harmonic analyses such as Fourier spectrum method on the excitation current in synchronous machines. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.