共轭Chen混沌系统的分岔分析及基于该系统的超混沌生成研究

分析了一个三维自治混沌系统的Hopf分岔现象,该系统的混沌吸引子属于共轭Chen混沌系统.通过引入一个控制器,基于该混沌系统构建了一个四维自治超混沌系统.该超混沌系统含有一个单参数,在一定的参数范围内呈现超混沌现象.通过Lyapunov指数和分岔分析,随着参数的变化该系统轨道呈现周期轨道、准周期轨道、混沌和超混沌的演化过程. 关键词： 混沌 超混沌生成 Hopf分岔 分岔分析     

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.     

基于线性矩阵不等式的一类新羽翼倍增混沌分析与控制

在对已有的混沌系统分析和研究的基础上,将一个二次混沌系统第三个方程关于x的线性项引入到第二个方程中,通过对该系统第二个等式中的线性项x作绝对值运算,提出了一类新的二次非线性系统.采用非线性动力学方法分析了系统参数变化时所经历的稳定、准周期、混沌的过渡过程,模拟电路实验结果与Matlab数值仿真结果相一致.分析发现混沌态时绝对值运算后的系统比原系统的Lyapunov指数更大,并可将原系统的混沌吸引子由两个翼的拓扑结构变为四翼的拓扑结构,从而实现羽翼倍增.针对该混沌特性更强的羽翼倍增混沌系统,基于Takagi-Sugeno(T-S)模糊模型和线性矩阵不等式(LMI),设计出使该羽翼倍增混沌系统渐近稳定的鲁棒模糊控制器.仿真结果证实了所提出定理和设计控制器的有效性.     

一类含Mathieu-Duffing振子的相对转动系统的分岔和混沌

建立了一类具有Mathieu-Duffing振子的两质量相对转动系统的非线性动力学方程. 应用多尺度法求解该系统发生主共振-基本参数共振的分岔响应方程,并通过奇异性分析得到系统稳态响应的转迁集. 利用Melnikov方法讨论系统在外激扰动和参激扰动变化下的全局分岔和系统进入混沌状态的可能途径,得到外激和参激幅值变化下系统可能出现多次通向混沌的道路,获得系统发生混沌的必要条件. 最后采用数值方法验证了理论研究的有效性. 关键词： 相对转动 Mathieu-Duffing振子 混沌 Melnikov方法     

单参数Lorenz混沌系统的电路设计与实现

为了研究混沌系统的性质及其应用,采用分立元件设计并实现了单参数Lorenz混沌系统,系统参数与电路元件参数一一对应.通过调节电路中的可变电阻,观察到了该单参数系统的极限环、叉式分岔、倍周期分岔和混沌等动力学现象,以及该系统由倍周期分岔进入混沌的过程.研究了分数阶单参数Lorenz系统存在混沌的必要条件,找出了分数阶单参数Lorenz系统出现混沌的最低阶数以及最低阶数随系统参数变化的一般规律.电路仿真与电路实现研究表明,单参数Lorenz系统具有物理可实现性、丰富的动力学特性以及理论分析与实验结果的一致性.     

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     

The bifurcation threshold value of the chaos detection system for a weak signal＊

Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detectionsystem for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detectionare correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system fora weak signal is established by using the theory of linear differential equation with periodic coefficients and computingthe Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system isdefined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of thechaos detection svstem.     

一类含时变间隙的强非线性相对转动系统分岔和混沌

建立一类具有时变间隙的两质量相对转动系统的强非线性动力学方程.应用MLP方法求解出变换参数,并运用多尺度法求解该系统发生1/2亚谐共振时的分岔响应方程,采用奇异性理论分析得到系统稳态响应的转迁集,并且得到系统在非自治情形下的分岔特性以及系统的分岔形态.最后通过数值仿真得到系统在间隙和阻尼参数变化下的分岔和混沌行为,发现随着系统参数变化系统将出现周期运动、倍周期运动以及混沌等多种不同的运动形态.     

Hopf bifurcation and uncontrolled stochastic traffic- induced chaos in an RED-AQM congestion control system

We study the Hopf bifurcation and the chaos phenomena in a random early detection-based active queue management (RED-AQM) congestion control system with a communication delay. We prove that there is a critical value of the communication delay for the stability of the RED-AQM control system. Furthermore, we show that the system will lose its stability and Hopf bifurcations will occur when the delay exceeds the critical value. When the delay is close to its critical value, we demonstrate that typical chaos patterns may be induced by the uncontrolled stochastic traffic in the RED-AQM control system even if the system is still stable, which reveals a new route to the chaos besides the bifurcation in the network congestion control system. Numerical simulations are given to illustrate the theoretical results.     

一个简单延迟非线性系统的动力学行为及混沌同步

分析一个简单二阶延迟系统的Hopf分支和混沌特性, 包括分支点、分支方向和分支周期解的稳定性, 解析求出退延迟情况下, 这个系统的相轨线方程; 通过数值计算并绘制分岔图, 揭示系统存在由倍周期通向混沌的道路; 利用单路线性组合信号, 反馈控制实现系统的部分完全同步; 利用主动-被动与线性反馈的联合, 实现系统的完全同步; 设计和搭建系统的电子实验线路, 并从实验中观测到与理论分析或数值计算相一致的结果. 关键词： 延迟非线性系统 电路实验 Hopf分支 混沌     

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.     

Dynamic Modeling and Chaos Control of Informatization Development in Manufacturing Enterprises

To explore the cooperative evolutionary mechanism among top management support, employees’ technical ability, and informatization performance in the process of the “integration of informatization and industrialization (IOII)” in manufacturing enterprises, this study established a three-dimensional dynamic model of informatization development, obtained the model parameters by the expert scoring method of case companies, and analyzed the time series of the dynamic model. After adjusting those parameters of the evolutionary process that do not meet the expectations of the enterprise, combined with management practice, the dynamic system is finally stable at the expected value. For a special state in the evolutionary process, the maximum Lyapunov exponent is used to identify the chaotic characteristics of the system, and a linear controller is designed to manage and control the chaotic system so that it evolves toward the expected value. The results of the case analysis verify the rationality of the model and the effectiveness of the control method, reveal the internal evolutionary mechanism of the informatization development of manufacturing enterprises, and explain the influence of chaos on enterprise management so as to help managers to use and control chaos.     

线性延时反馈Josephson结的Hopf分岔和混沌化

考虑线性延时反馈控制下电阻-电容分路的Josephson结,运用非线性动力学理论分析了受控系统平凡解的稳定性.理论分析表明,随着控制参数的改变,系统的稳定平凡解将会通过Hopf分岔失稳,并推导了发生Hopf分岔的临界参数条件.对不同参数条件下受控系统的动力学进行了数值分析.结果显示,系统由Hopf分岔产生的稳定周期解,将进一步通过对称破缺分岔和倍周期分岔通向混沌. 关键词： 约瑟夫森结 线性延时反馈 Hopf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     

The chaotic behavior analysis near the points B_3～B_5 of a nonlinear Fabry-Perot cavity

In this paper a further proof is given to the instability of 2~n bifurcation near the point B_3. The chaos in B_3 seems to arrive via the route of intermittent and tangential bifurcation. It is also shown that a metastability chaos occurs in the transition from B_4 to B_5.     

Nonlinear parametrically excited vibration and active control of gear pair system with time-varying characteristic

In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.     

Bifurcation and chaos behavior of intracavity acousto-optic modulation laser system

In this paper,based on the behavior of acousto-optic modulator,we have anal-ysed the instability of an intracavity acousto-optic modulation(IAOM)laser system with afeedback device.The bifurcation and chaos behavior of the system is discussed in detail to ob-tain some quantitative results.     

基于Hamilton模型的永磁同步风力发电系统中混沌运动的H∞控制

针对永磁同步风力发电系统的混沌运动现象, 提出了基于系统Hamilton模型的H_∞控制方案, 使得系统脱离混沌, 运行稳定. 首先将永磁同步风力发电系统模型经过一系列状态变换, 转化为类Lorenz经典数学模型, 并验证了系统在一定参数区域内存在混沌现象. 随后基于Hamilton系统充分利用系统物理结构和无需补偿“无功力”的优点, 建立了混沌系统的Hamilton模型, 并考虑了系统存在外扰情况下的H_∞控制方法. 本文所设计的控制器     

Feedback Induced Instability and Chaos in Semiconductor Lasers and Their Applications

Semiconductor laser with feedback is an excellent model for nonlinear optical system which shows chaotic dynamics. It is interesting not only from the fundamental physical study but also application standpoints of view. The dynamics of feedback induced instability and chaos, especially for optical feedback, and their applications are reviewed in this paper. The model of such a system is described by the laser rate equations. At first the dynamic behaviors of feedback induced instability and chaos in semiconductor lasers are discussed on the basis of the theory and experiments. Instability and chaos may be stabilized by the method of chaos control. Then we apply the method to suppress the noise induced by the feedback in a semiconductor laser. The synchronization of chaos between two similar systems is also an important issue in chaos applications and we discuss secure communications based on chaos synchronization. Some other examples of applications of feedback induced chaos are also described.     

基于自适应斜坡补偿的双环电流模DC/DC混沌控制

提出了一种自适应斜坡补偿方法,将该方法引入到双环电流模buckDC/DC的混沌控制中,并给出实现该方法的电路结构.建立了双环电流模DC/DC系统稳定性分析的离散模型,理论分析了自适应斜坡补偿在双环控制下系统的稳定性条件,推导出了自适应因子k与系统工作的最大占空比的关系式.仿真结果表明该方法可有效控制系统的分岔和混沌现象,提高系统的工作范围和动态响应速度.