轴压下非线性材料板条混沌运动区域分析

研究了轴下非线性材料板条的混沌运动,并讨论了分析轴向压力、板条几何参数及多频外扰力对非线性材料板条发生混沌运动区域的影响。     

碰撞阻尼器系统的分岔、混沌与控制

对碰撞阻尼器振动系统推导了周期解存在的条件，并利用Poincare映射和数字仿真进行了分岔与混沌运动的研究。计算结果表明，这种非线性碰撞振动系统在特定的参数条件下，除了稳定的周期运动形态外，还会沿着倍周期分岔、HOPF分岔及拟周期环面破裂等分岔进入混沌运动。因此，为了有效地利用碰撞阻尼器特性控制振动，在设计和使用碰撞阻尼器时应考虑参数满足周期运动的条件，避免由于自身的非线性特性而产生的混沌运动。     

碰撞振动系统的参数自调节混沌控制

针对含间隙碰撞振动系统由于系统参数的变化，发生分岔和混沌这一实际情况，提出了系统参数依据系统输出的变化自动调节连续反馈控制的策略。给出了参数自调节的控制律，选取适当的控制强度向量，混沌运动可被引导到稳定的目标周期轨道。对一两自由度含间隙碰撞振动系统进行数值模拟，验证了这一策略的有效性。     

采用BP神经网络进行混沌运动控制

利用4层BP神经网络对非线性非连续函数的无穷逼近特性，设计了控制方法，对非线性系统的混沌运动进行控制。在系统发生混沌运动时，对于不同类型的期望信号，可以将不同自由度的混沌运动分别控制到各自的目标信号上。目标函数可以是周期函数，非线性函数。对Lorenz方程进行了仿真计算，结果显示可以将混沌运动控制到锯齿波信号、正弦信号和直流信号上；对Rossler方程的仿真计算，可以将系统的混沌运动控制到方波信号与直流信号上，控制所用的时间很短。     

考虑损伤双层扁球面网壳的非线性动力学特性

基于Lematire等效应变损伤理论,计及扁球面网壳各个杆件的损伤影响,应用拟壳法导出了具有损伤的扁球面网壳的动力学非线性控制方程。提出了以中心最大振幅为摄动参数的摄动-变分法的求解方法,对动力非线性控制方程进行了求解,得出了相应的物理量的解析式。据此进行数值分析,得出了相应的特征关系。并用Galerkin方法导出了一个含二次和三次非线性振动微分方程并求解了具有损伤扁球面网壳的的非线性动力学的自由振动方程,给出了准确解。而后利用Melnikov函数法,从理论上给出了考虑损伤的系统发生混沌运动的临界条件,并通过计算机数字仿真证实了考虑损伤的扁球面网壳在非线性强迫振动时存在混沌运动,同时发现损伤使得系统更易发生混沌运动。     

基于分形和子波变换自适应控制混沌

在自适应控制混沌方法的基础上结合子波分析、分形理论，提出了一种自适应控制受迫Ｄｕｆｉｎｇ振子的混沌运动的方法。克服了需要预先知道系统的具体动力学模型及需要设计一个参考模型等缺陷。从实验中即可测得系统的某个输出量，引入外力控制混沌运动。数值分析表明在适当的控制信号下，混沌运动得到了很好的控制。     

双频激励下含分数阶非线性汽车悬架系统的混沌研究

研究了含分数阶非线性特性的1/4 汽车悬架模型在双频激励下的混沌运动。运用Melnikov 方法,推导出系统发生异宿混沌运动的解析必要条件,得到系统混沌边界曲面阈值,讨论了悬架系统各参数对混沌边界曲面的影响。运用时间历程图、频谱图、相图、庞加莱截面图及最大李雅普诺夫指数进行数值验证。研究表明,在双频激励下悬架系统存在混沌运动,且含分数阶非线性悬架系统中阻尼系数、刚度系数等各参数对混沌边界曲面阈值都有一定影响,其中分数阶项阶数和系数及线性阻尼系数对其影响较大。     

OGY法控制混沌研究

OGY法是一种有效的混沌控制方法，其利用混沌运动对微小扰动极端敏感及遍历特性，通过系统参数的微小摄动将混沌控制到期望的轨道，文中对OGY法及其两种改进方法作了介绍，进行数值仿真，比较3种方法的差异。为今后的混沌控制研究方法指出了新的方向。     

控制混沌及超混沌

提出的自适应校正方法既适用于控制混沌系统又适用于控制超混沌系统，不需关于体系动力学的知识也不需要任何人部的控制参数。作者先系统地推导出了反馈矩阵的具体形式，进而将该方法应用到混沌Henon系统和一个超混沌系统，模拟结果表明，受控的不稳定轨道都以指数速率趋于预定点。     

冲击消振系统动力学初探

通过数值分析获得冲击消振系统典型的稳定周期响应相轨图,在相轨图中直接观察倍周期分叉,并在庞加莱（Poincare）截面中显示了该振冲系统的混沌运动性质。     

Delayed feedback control of chaos

Time-delayed feedback control is well known as a practical method for stabilizing unstable periodic orbits embedded in chaotic attractors. The method is based on applying feedback perturbation proportional to the deviation of the current state of the system from its state one period in the past, so that the control signal vanishes when the stabilization of the target orbit is attained. A brief review on experimental implementations, applications for theoretical models and most important modifications of the method is presented. Recent advancements in the theory, as well as an idea of using an unstable degree of freedom in a feedback loop to avoid a well-known topological limitation of the method, are described in detail.     

Estimating delay from a dynamical system response to a weak pulsed action

A new method is proposed for estimating the delay time of a delayed-feedback system, which is based on an analysis of the system response to a weak external perturbation in the form of rectangular pulses. The method is applicable to systems that perform both periodic and chaotic oscillations. The efficiency of the proposed procedure is demonstrated based on numerical examples and for the experimental time series of a real radiophysical system.     

基于神经网络反馈控制的混沌运动的仿真研究

摘要：本文应用神经网络反馈控制策略,对混沌系统进行控制研究。首先利用神经网络能够高精度逼近非线性系统的特点,通过系统辨识建立要研究的混沌系统的神经网络模型,然后控制器应用此系统模型对混沌运动进行反馈线性化控制,将混沌吸引子中的不稳定周期轨道镇定到不动点,或诱导到各个周期轨道。对Lorenz混沌系统的仿真结果表明,神经网络反馈控制混沌的方法具有有效性。     

Liu-cos混沌系统在声波弱信号检测中的应用

针对混沌三维弱信号检测系统的特点,设计了一种傅里叶变换和李雅普诺夫算法相结合的收敛性判别算法,证明了三维Liu-cos混沌系统对于声波弱信号检测具有广域性并且当输入声波信号幅值大于临界阈值时,系统变量x输出平衡于输入的周期摄动力信号, 系统变量y和z的输出收敛于零,临界阈值具有唯一性。解决了传统Duffing混沌系统应用于声波弱信号检测时,系统变量x和y输出不收敛、只能进入窄域检测等问题。构造了Duffing混沌系统和三维Liu-cos混沌系统的实际声波检测实验,分析了混沌系统在实际声波检测过程中的性能。     

控制Mathieu方程中混沌的三种方法分析

利用数值仿真的方法，对一类Mathieu方程一欧拉动弯曲问题进行了研究．利用分岔图、相图等揭示了该系统经由倍周期分岔通向混沌的路径，另用时间响应图、相图和功率谱图来表明系统非线性状态．通过分岔图来选择适当的控制参数，利用耦合控制法、x｜x｜控制法和周期激振力控制法对欧拉动弯曲问题中的混沌行为进行了有效的控制．结果表明，通过这三种方法，都可以将系统的混沌运动控制到稳定的周期轨道。     

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。     

Attractor selection in a modulated laser and in the Lorenz circuit

By tuning a control parameter, a chaotic system can either display two or more attractors (generalized multistability) or exhibit an interior crisis, whereby a chaotic attractor suddenly expands to include the region of an unstable orbit (bursting regime).Recently, control of multistability and bursting have been experimentally proved in a modulated class B laser by means of a feedback method. In a bistable regime, the method relies on the knowledge of the frequency components of the two attractors. Near an interior crisis, the method requires retrieval of the unstable orbit colliding with the chaotic attractor.We also show that a suitable parameter modulation is able to control bistability in the Lorenz system. We observe that, for every given modulation frequency, the chaotic attractor is destroyed under a boundary crisis. The threshold control amplitude depends on the control frequency and the location of the operating point in the bistable regime. Beyond the boundary crisis, the system remains in the steady state even if the control is switched off, demonstrating control of bistability.     

Synchronization in a steer-by-wire vehicle dynamic system

This work verifies the chaotic motion of a steer-by-wire vehicle dynamic system, and then elucidates an application of the synchronization to a vehicle model to control the chaos. The largest Lyapunov exponent is estimated from the synchronization to identify periodic and chaotic motions. Then, a bifurcation diagram reveals complex nonlinear behaviors over a range of parameter values. Finally, a continuous feedback control method based on the synchronization characteristics is presented to control a chaotic vehicle handling and steering system. The designed controller is demonstrated to work quite well for nonlinear systems in achieving robust stability and protecting the vehicle from slip or spin. Some simulation results are presented to establish the feasibility of the proposed method.     

Chaos and nonlinear stochastic dynamics

This article presents a discussion of certain aspects of the interrelationship between the chaotic response of some deterministic nonlinear dynamic system and the stochastic response of the corresponding system obtained by introducing a stochastic perturbation in the form of additive Gaussian white noise. The state space vector of the latter system can then often be represented as a Markov diffusion process. The joint probability density function of the state space vector of this Markov process is closely related to the corresponding chaotic attractor of the underlying deterministic system, and it will be demonstrated that it can be effectively used for prediction purposes.     

Nonlinear analysis of an elastic cable under harmonic excitation

The nonlinear behavior of an elastic cable subjected to harmonic excitation is studied and solved. The method of multiple scales perturbation is applied to analyze the response of the nonlinear system near the simultaneous principle primary and internal resonance. The stability of the proposed analytic nonlinear solution near the simultaneous primary-internal resonance is studied and the stability condition is investigated. The effect of different parameters on the steady state responses of the vibrating system is studied and discussed using frequency response equations. The numerical solutions and chaotic response of the nonlinear system of the elastic cable for different parameters are also studied.