Langford系统Hopf分叉的线性反馈控制

分析Langford系统的Hopf分叉现象，并研究采用线性反馈控制方法控制该系统的Hopf分叉.从理论上推导出受控系统产生Hopf分叉的条件，给出了某些极限环的解析表达式，对该系统进行了分叉点的转移与极限环的稳定性控制.数值模拟说明本文采用的方法对Langford系统的Hopf分叉控制是有效的. 关键词： Langford系统 反馈控制 Hopf分叉 极限环     

一类相对转动系统Hopf分岔的非线性反馈控制

研究一类非线性摩擦阻尼力作用下的相对转动系统的Hopf分岔现象,给出系统产生Hopf分岔的充要条件,提出一种非线性反馈控制方法对系统的Hopf分岔点进行转移,并控制极限环的稳定性和幅值,数值模拟说明该方法对一类相对转动系统的Hopf分岔控制是有效的. 关键词： 相对转动 非线性反馈控制 Hopf分岔 极限环     

一类相对转动时滞非线性动力系统的稳定性分析

建立了具有时变刚度、非线性阻尼和谐波激励的一类相对转动时滞非线性动力系统的动力学方程.采用多尺度法推导出时滞动力系统的分岔响应方程,运用奇异性理论研究系统结构稳定性,得到主共振稳态响应方程的转迁集以及不同参数下分岔曲线的拓扑结构.应用Hopf分岔理论讨论了时滞动力系统动态稳定性,给出了系统产生极限环的条件,最后用数值模拟的方法研究了时滞参数对系统极限环幅值的影响。     

耦合的van der Pol振子的极限环幅值控制

设计反馈控制器，对一类耦合的van der Pol振子的极限环幅值进行控制. 用近似解析方法求出了控制系统的幅值的控制方程, 得到了控制参数与极限环幅值的函数关系, 使系统的振幅能按需求得到有效地调整. 通过数值计算绘制了在不同控制参数下, 系统响应的时间历程曲线和极限环. 近似解析方法计算得到的结果与数值计算进行了比较，两者是符合的. 这一方法也可以推广应用到其他耦合的van der Pol振子.     

一类准周期参激非线性相对转动动力系统的稳定性与时滞反馈控制

建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程. 采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性. 在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响. 采用时滞反馈控制的方法对系统分岔和极限环(域)进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环(域)的幅值和稳定性. 关键词： 相对转动 准周期参激 时滞反馈 极限环     

一类耦合非线性相对转动系统的Hopf分岔控制

建立一类耦合非线性相对转动系统的动力学方程,研究系统在主共振和1∶1内共振情况下的Hopf分岔行为,设计非线性反馈控制器,控制系统Hopf分岔的发生、极限环的稳定性和幅值,数值模拟证明了该方法的有效性.     

行波管放大器中辐射场的极限环振荡和混沌

以行波管放大器中辐射场的非线性不稳定阈值分析为基础，对辐射场从频率分叉到混沌的演化过程和不同区域这些非线性不稳定态的时间特性和频率特性进行了研究.在“软”非线性区域，辐射场表现为极限环振荡和频率分岔，频谱是离散的且相对于载波频率是不对称的.这种不稳定是阵发性的，适当的调节控制参量，可使器件工作在所需的定态或极限环振荡态上；在“硬”非线性区域，辐射场表现为非周期的随机振荡和频率混沌，频谱连续且频带很宽，场幅值较大的成分集中在接近于零频的低频范围里.这种不稳定是连续性的，不能通过调节参量来消除. 关键词： 行波管 辐射场 分岔 极限环 混沌     

单频外激励弹簧摆的鞍结分岔控制

对弹簧摆的振动幅值控制进行研究,设计了反馈控制器,对弱非线性系统用近似解析方法求出了控制系统的幅值控制方程,得到了控制参数与幅值的函数关系,使多自由度非线性系统的鞍结分岔得到控制.这项工作可以推广到其他多自由度非线性系统的分岔控制. 关键词： 外激励弹簧摆 鞍结分岔 振动幅值 反馈控制     

黎开管中热声拍振现象及其主动控制

黎开管中燃烧振荡现象的实验研究发现,在不稳定发生的极限工况附近可能存在幅值周期性变化的振荡现象,也即拍振,其拍频可低于l Hz。本文比较了铁丝网和穿孔陶瓷两种稳焰体对拍振发生的影响;通过时频分析揭示了拍振的声压脉动的主频随时间周期性变化的特征。采用基于数字信号处理器的控制系统,研究了对极限环和拍振的主动控制效果,实验结果表明,黎开管系统中导致拍振的非线性可能使得采用常规主动控制方法难以取得满意的控制效果。     

周期驱动下半导体动力学行为及控制

从nGaAs载流子非线性输运理论出发,建立物理模型,推导其动力学方程,分析系统随外场变化出现的复杂分支情况.数值模拟表明,在输入场幅值和频率变化的一定范围内,该系统具有周期、准周期和混沌特性,计算了表征混沌特性的物理量.利用间隙脉冲驱动法控制混沌得到预期的周期轨道 关键词： 分支 混沌 负微分电导     

Bifurcation analysis and control of periodic solutions changing into invariant tori in Langford system

Bifurcation characteristics of the Langford system in a general form are systematically analysed, and nonlinear controls of periodic solutions changing into invariant tori in this system are achieved. Analytical relationship between control gain and bifurcation parameter is obtained. Bifurcation diagrams are drawn, showing the results of control for secondary Hopf bifurcation and sequences of bifurcations route to chaos. Numerical simulations of quasi-periodic tori validate analytic predictions.     

单自由度非线性保守系统作大振幅振动时周期的计算方法

简要介绍了单自由度非线性保守系统作大振幅振动时周期的计算方法,并给出了几个常见典型振动问题的周期公式．     

A multidimensional superposition principle: numerical simulation and analysis of soliton invariant manifolds I

Abstract

In the framework of a multidimensional superposition principle involving an analytical approach to nonlinear PDEs, a numerical technique for the analysis of soliton invariant manifolds is developed. This experimental methodology is based on the use of computer simulation data of soliton–perturbation interactions in a system under investigation, and it allows the determination of the dimensionality of similar manifolds and partially (in the small amplitude perturbation limit) to restore the related superposition formulae. Its application for cases of infinite dimensionality, and the question of approximation by lower dimensional manifolds and, respectively, by superposition formulae of a lower order are considered as well. The ideas and implementation details are illustrated and verified by using examples with the integrable, MKdV and KdV equations, and also nonintegrable, Kawahara and Regularized Long Waves equation, soliton models.     

Amplitude control of limit cycle in a van der Pol Duffing system

This paper applies washout filter technology to amplitude control of limit cycles emerging from Hopf bifurcation of the van der Pol--Duffing system. The controlling parameters for the appearance of Hopf bifurcation are given by the Routh--Hurwitz criteria. Noticeably, numerical simulation indicates that the controllers control the amplitude of limit cycles not only of the weakly nonlinear van der Pol--Duffing system but also of the strongly nonlinear van der Pol--Duffing system. In particular, the emergence of Hopf bifurcation can be controlled by a suitable choice of controlling parameters. Gain-amplitude curves of controlled systems are also drawn.     

Response control for the externally excited van der Pol oscillator with non-local feedback

A non-local control force is introduced in such a way to obtain a third-order nonlinear differential equation (jerk dynamics) and to control nonlinear vibrations in an externally excited van der Pol oscillator. Two first-order nonlinear ordinary differential equations governing the modulation of the amplitude and the phase of solutions are derived and subsequently the performance of the control strategy is investigated. Excitation amplitude–response and frequency–response curves are shown. In certain cases when the excitation amplitude is very low an approximate analytic solution corresponding to a modulated two-period quasi-periodic motion can be obtained for the uncontrolled system. Uncontrolled and controlled systems are compared and the appropriate choices for the feedback gains are found in order to reduce the amplitude peak of the response and to exclude the possibility of quasi-periodic motion. Numerical simulation confirms the validity of the new method.     

Self-excited oscillation under nonlinear feedback with time-delay

Several important applications use nonlinear feedback methods for synthetically inducing self-excited oscillations in mechanical systems. The van der Pol and saturation function type feedback methods are widely used. The effects of time-delay on the self-excited oscillation of single and two degrees-of-freedom systems under nonlinear feedback have been studied in this paper. It is shown that a single degree-of-freedom oscillator with the van der Pol type nonlinear feedback can produce unbounded response in presence of time-delay. In general, an uncontrolled time-delay in the feedback changes the state of oscillations in an uncertain manner. Therefore, a bounded saturation type feedback with controllable time-delay is proposed for inducing self-excited oscillations. The feedback signal is essentially an infinite weighted sum of a nonlinear function of the state variables of the system measured at equal intervals in the past. More recent is the measurement, higher is the weight. Thus, the feedback signal uses a large amount of information about the past history of the dynamics. Such a control signal can be realized in practice by a recursive means. The control law allows three parameters to be varied namely, the time-delay, feedback and recursive gains. Multiple time scale analysis is used to plot amplitude vs. time-delay curves. Time-delay can be controlled to vary the amplitude of oscillation as well as to switch the oscillation from one mode to the other in a two degrees-of-freedom system. It is shown that a higher recursive gain can exercise a better and a more robust control on the amplitude of oscillation of the system. Analytical results are compared with the results of numerical simulations.     

On the nonlinear primary resonances of a piezoelectric laminated micro system under electrostatic control voltage

In this article, a comprehensive nonlinear analysis for a piezoelectric laminated micro system around its static deflection is presented. This static deflection is created by an electrostatic DC control voltage through an electrode plate. The micro system beam is assumed as an elastic Euler-Bernoulli beam with clamped-free end conditions. The dynamic equations of this model have been derived by using the Hamilton method and considering the nonlinear inertia, curvature, piezoelectric and electrostatic terms. The static and dynamic solutions have been achieved by using the Galerkin method and the multiple-scales perturbation approach, respectively. The results are compared with numerical and other existing experimental results. By studying the primary resonance excitation, the effects of different parameters such as geometry, material and excitations voltage on the system?s softening and hardening behaviors are evaluated. In a piezoelectrically actuated micro system it was showed that because of existence of curvature and inertia nonlinear terms a small change in excitation amplitude can lead to the formation and expansion of nonlinear response. In this paper, it is demonstrated that by applying an electrostatic DC control voltage, these nonlinearities can be controlled and altered to a linear domain. This model can be used to design a nano or micro-scale smart device.     

Sound generation by spheroidal metallic nanoclusters embedded in transparent matrix under the action of laser pulses

The theory of the photo-acoustical effect caused by a laser action on metal nanoclusters embedded in a dielectric matrix is build. The energy absorbed by clusters propagates through the dielectric matrix and generates the sound waves in it via the thermodeformation mechanism. The formulae for an acoustical signal are derived, and the high sensitivity of the sound wave amplitude to the shape of metal clusters, as well to such parameters of a laser irradiation as the frequency, polarization, and intensity, is revealed. The behavior of the sound vibrations amplitude in a region of the surface plasmons absorption is studied in detail. It is found that this amplitude at light absorption by a discrete metal film (a system of clusters in the matrix) can exceed the corresponding amplitude for the absorption by a continuous metal film in the region of plasmon resonances by several orders of magnitude.     

深光晶格势阱中凝聚体的扭结包络隙孤子

发展准离散多尺度法结合紧束缚近似,解析地研究了局陷于光晶格势阱中凝聚体的非线性动力学性质.结果发现,系统中出现稳定的对称包络孤子外,还可观察到一种新的非线性元激发:扭结包络隙孤子.有趣的是,该隙孤子并不传播且局域在初始位置,其幅度可通过光晶格势阱的晶格常数和势阱深度来调控.相应的实验方案是:通过改变形成光晶格势阱的两交叉耦合激光束之间的夹角和(或)激光光强来调控扭结包络隙孤子的幅度.