一类由饱和引起的非线性现象

以一个功率因数校正boost变换器为例,描述了当系统在饱和与非饱和状态间不断切换时出现的一类非线性现象,分析了这些现象的特点和产生原因.推导了考虑饱和的分段微分方程,并据此进行了仿真,结果表明,系统一方面会出现倍周期分岔和混沌等传统的非线性现象,另一方面由于整流输入电流碰到饱和边界,系统的定性行为发生突变,会出现边界碰撞分岔,还能从混沌直接变为周期1.这类由饱和引起的非线性现象及相关分析得到了实验验证. 关键词： 饱和 非线性 分岔 混沌     

基于符号序列描述的一类分段光滑系统中分岔现象与混沌分析

从拓扑序列出发，提出了描述DC/DC变换器一类分段光滑系统中的分岔现象和混沌行为的符号序列方法，根据最大子序列的性态判别分岔的类型，以及检测边界碰撞分岔的发生.例如,当发生倍周期分岔时，最大子序列保持不变；当发生边界碰撞分岔时，最大子序列发生变化；混沌态则没有最大子序列.研究表明，占空比是表征DC/DC变换器一类分段光滑系统动力学行为的一个最本质的量，“饱和非线性”是引起边界碰撞分岔产生的根本原因. 关键词： 符号序列 分岔 混沌 分段光滑系统     

一类非线性相对转动系统的组合谐波分岔行为研究

针对一类具有非线性刚度、非线性阻尼的非线性相对转动系统, 应用耗散系统的拉格朗日原理建立在组合谐波激励作用下非线性相对转动系统的动力学方程. 构造李雅普诺夫函数, 分析相对转动系统的稳定性, 研究自治系统的分岔特性. 应用多尺度法求解相对转动系统的非自治系统在组合激励作用下的分岔响应方程. 最后采用数值仿真方法, 通过分岔图、时域波形、相平面图、Poincaré截面图等研究外扰激励、系统阻尼、 非线性刚度对相对转动系统经历倍周期分岔进入混沌运动的影响. 关键词： 相对转动 组合激励 分岔 混沌     

V2控制Buck变换器分岔与混沌行为的机理及镇定

V²控制的Buck变换器在反馈放大系数变化的情况下表现出丰富的非线性行为. 本文建立了V²控制Buck变换器的离散迭代模型, 利用单值矩阵方法研究了系统不稳定行为. 随着反馈放大系数的增大, 变换器从稳定的周期一状态发生一系列的倍周期分岔现象进入周期二、周期四, 不断倍化直至混沌态. 同时其单值矩阵的最大特征值也沿着实负轴穿越单位圆, 从而从稳定性的角度揭示了系统发生一系列倍周期分岔的机理. 基于单值矩阵理论, 利用正弦电压补偿方法镇定了系统的分岔和混沌行为, 得到了镇定后系统的稳定边界. 仿真和实验结果证明了本文分析方法和结论的正确性. 关键词： V²控制')" href="#">V²控制 Buck变换器 分岔 镇定控制     

非线性环形光学腔中分岔混沌的新行为

利用数值模拟方法研究了非线性环形光学腔中的Ikeda方程,发现:长延时下,分岔图的拓扑结构、分岔方式、收敛速率以及周期窗口的结构都随参数B,φ₀的取值不同而异。短延时下,通过适当近似,将Ikeda方程化为带有一定记亿效应的迭代映象,所得到的近似系统显示出非倍周期分岔行为,并伴有一些奇特的周期窗口,混沌区中的无限嵌套的自相似结构变得模糊,不易分辨。 关键词：     

非线性自治系统频率特性及其利用

用数值模拟方法对三维非线性混沌系统进行了分析,发现衰减项参量的变化基本不影响系统的周期(指在同一周期内),并且系统基频与分频(基本周期与倍周期)之间还存在着近似的简单倍数关系.另外,还将Hopf分支理论中的实用分析方法应用到某些系统,解析地确定出系统开始出现稳定周期解(分岔)的临界位置、基本周期的近似值及分岔方向等有关特征量.进一步利用确定系统基本周期的方法以及基本周期和其他周期关系的规律,讨论了变量延迟反馈法控制混沌的两个实例 关键词： 自治系统 基本周期(频率) Hopf分支 混沌控制     

非线性切换系统的动力学行为分析

建立了周期切换下的非线性电路模型,基于子系统平衡点及其稳定性分析,分别给出了其相应的fold分岔和Hopf分岔条件,讨论了子系统在不同平衡态下由周期切换导致的各种复杂行为,指出切换系统的周期解随参数的变化存在着倍周期分岔和鞍结分岔两种失稳情形,并相应地导致不同的混沌振荡,进而结合系统轨迹及其相应的分岔分析,揭示了各种振荡模式的动力学机理. 关键词： 周期切换 倍周期分岔 鞍结分岔 混沌     

超混沌Lorenz系统

对Lorenz系统添加一个非线性控制器，使之构成四维超混沌Lorenz系统.利用分岔图、Lyapunov指数谱及相图分析方法，研究了超混沌Lorenz系统的运动规律.数值模拟结果表明：新引入参数处于不同取值范围时，超混沌Lorenz系统可以分别呈现收敛、发散、周期、混沌及超混沌动力学行为. 关键词： Lorenz系统 超混沌 Lyapunov指数 分岔     

耦合电路中的复杂振荡行为分析

讨论了两个非线性电路适当连接后的耦合系统随耦合强度变化的演化过程.给出了两子系统各自的分岔行为及通向混沌的过程,指出原子系统均为周期运动时,耦合系统依然会由倍周期分岔进入混沌,同时在混沌区域中存在有周期急剧增加及周期增加分岔等现象.而当周期运动和混沌振荡相互作用时,在弱耦合条件下,受混沌子系统的影响,原周期子系统会在其原先的轨道邻域内作微幅振荡,其振荡幅值随耦合强度的增加而增大,混沌的特征越加明显,相反,周期子系统不仅可以导致混沌子系统的失稳,也会引起混沌吸引子结构的变化. 关键词： 非线性电路 耦合强度 分岔 混沌     

一类相对转动非线性动力系统的混沌运动

研究一类具有同宿轨道、异宿轨道的相对转动非线性动力系统的混沌运动. 建立具有非线性刚度、非线性阻尼和外扰激励作用的一类两质量相对转动非线性动力系统的动力学方程. 利用Melnikov方法讨论了系统的全局分岔和系统进入混沌状态的可能途径,给出了系统发生混沌的必要条件,并利用最大Lyapunov指数图,分岔图,Poincare截面图和相轨迹图进一步分析了系统的混沌行为. 关键词： 相对转动 非线性动力系统 混沌 Melnikov方法     

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.     

平面单位区域内二次曲线混沌特性研究

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.     

Magneto-elastic dynamics and bifurcation of rotating annular plate

In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton's principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-anotherside. Poincare′ maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions,and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos.     

空间单位区域双二次有理贝赛尔曲面混沌特性研究

研究空间单位区域内两个二次曲面映射构成的函数的混沌特性, 发现了一种构造混沌的方法. 当一个曲面是单位区域内标准曲面, 另一个曲面随机生成时, 此函数是混沌的概率可以大于十分之一, 说明在满足一定条件时, 混沌是极其普遍的. 通过计算Lyapunov指数以及绘制分岔图等对该类函数的混沌特性进行分析, 根据参数变化的分岔图以及混沌曲面控制点的区域分布特性等寻找混沌映射函数, 得到了大量的二维混沌吸引子图形, 并对其中三个进行了详细研究. 另外, 把灰度图像作为离散二维函数, 首次研究了图像作为迭代表达式时表现出的一些混沌特性. 研究发现, 相同的或者相近的图像易于收敛到周期点上, 这个结果可以用于图像识别等研究领域. 关键词： 混沌 迭代 图像     

Suppression of chaos and other dynamical transitions induced by intercellular coupling in a model for cyclic AMP signaling in Dictyostelium cells

The effect of intercellular coupling on the switching between periodic behavior and chaos is investigated in a model for cAMP oscillations in Dictyostelium cells. We first analyze the dynamic behavior of a homogeneous cell population which is governed by a three-variable differential system for which bifurcation diagrams are obtained as a function of two control parameters. We then consider the mixing of two populations behaving in a chaotic and periodic manner, respectively. Cells are coupled through the sharing of a common chemical intermediate, extracellular cAMP, which controls its production and release by the cells into the extracellular medium; the dynamics of the mixed suspension is governed by a five-variable differential system. When the two cell populations differ by the value of a single parameter which measures the activity of the enzyme that degrades extracellular cAMP, the bifurcation diagram established for the three-variable homogeneous population can be used to predict the dynamic behavior of the mixed suspension. The analysis shows that a small proportion of periodic cells can suppress chaos in the mixed suspension. Such a fragility of chaos originates from the relative smallness of the domain of aperiodic oscillations in parameter space. The bifurcation diagram is used to obtain the minimum fraction of periodic cells suppressing chaos. These results are related to the suppression of chaos by the small-amplitude periodic forcing of a strange attractor. Numerical simulations further show how the coupling of periodic cells with chaotic cells can produce chaos, bursting, simple periodic oscillations, or a stable steady state; the coupling between two populations at steady state can produce similar modes of dynamic behavior.     

Spatiotemporal chaos synchronization of an uncertain network based on sliding mode control

The sliding mode control method is used to study spatiotemporal chaos synchronization of an uncertain network.The method is extended from synchronization between two chaotic systems to the synchronization of complex network composed of N spatiotemporal chaotic systems.The sliding surface of the network and the control input are designed.Furthermore,the effectiveness of the method is analysed based on the stability theory.The Burgers equation with spatiotemporal chaos behavior is taken as an example to simulate the experiment.It is found that the synchronization performance of the network is very stable.     

Circuitry implementation of a novel four-dimensional nonautonomous hyperchaotic Liu system and its experimental studies on synchronization control

Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.     

CHAOS, CHAOS CONTROL AND SYNCHRONIZATION OF ELECTRO-MECHANICAL GYROSTAT SYSTEM

The dynamic behavior of electro-mechanical gyrostat system subjected to external disturbance is studied in this paper. By applying numerical results, phase diagrams, power spectrum, Period-T maps, and Lyapunov exponents are presented to observe periodic and chaotic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. Several methods, the delayed feedback control, adaptive control algorithm (ACA) control are used to control chaos effectively. Anticontrol of chaos destroyed the periodic motions and replaced by chaotic motion effectively by adding constant motor torque and adding periodic motor torque. Finally, synchronization of chaos in the electro-mechanical gyrostat system is studied.     

Period doubling toward chaos in a driven magnetic macrospin

The Landau-Lifshitz-Gilbert equation is analyzed in the case of a configuration involving easy plane isotropy under the influence of a sinusoidally oscillating magnetic field and a demagnetizing field. Through the use of numerical techniques, chaotic behavior is found and analyzed. By reducing the system to a discrete map (numerically), bifurcation diagrams for the system are computed. The system is found to exhibit a period doubling cascade route to chaos, and it obeys certain convergence rules for chaotic transitions outlined by Feigenbaum. A connection is drawn between the route to chaos and the geometry of the system, and comparisons are made with similar systems. Within the chaotic regime, windows of arbitrarily large period are suspected to exist, and explicitly illustrated and discussed for a period three window.     

Chaos control and synchronization in Bragg acousto-optic bistable systems driven by a separate chaotic system

In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.