一个五维超混沌系统Hopf分岔控制

本文以五维超混沌类Pan系统为研究对象,根据高维Hopf分岔理论和Routh-Hurwitz理论,分析了系统非零平衡点的稳定性,以及分岔解稳定性．采用Washout控制法,对系统设置非线性控制器进行Hopf分岔和稳定性控制．经过分析分别得到了分岔参数、稳定性参数与控制参数之间的对应关系．从对应关系可以得出,通过调节控制器的控制参数,可以使系统分岔参数、稳定性参数发生改变,即可实现系统Hopf分岔发生延迟,分岔解稳定性范围发生变化．数值仿真验证了理论分析的正确性．     

四维Qi系统的参数自适应控制

基于Routh-Hrtwitz稳定性理论及Hopf分岔理论分析了四维Qi系统第二类非零平衡点的动力学行为,并通过绘制分岔图及最大Lypunov指数谱验证理论分析结果。给出了基于系统变量为观测量的参数自适应控制器,该控制器能自动调整控制参数,在参数受到较大扰动的情况下保持系统渐近稳定,并利用Lyapunov直接方法证明了受控系统的全局稳定性。通过数值模拟证明了文中所给的控制方法具有较快的收敛速度。关键词：Qi系统 非零平衡点 参数自适应控制 参考模型     

一类非线性相对转动系统的动力学行为及其机理分析

研究了一类具有非线性刚度的相对转动系统的动力学行为。应用Routh-Hurwitz稳定性理论判断了相对转动系统平衡点的稳定性。应用分岔理论研究了平衡点失稳时的分岔行为,推导了平衡点产生fold分岔的条件,进而通过仿真得到了平衡点在双参数平面上的分岔集及单参数分岔曲线,研究了不同参数区域内平衡点的个数以及稳定性问题。应用分岔图研究了相对转动系统随平方非线性刚度系数及激励角频率变化的全局动力学行为,获得了周期三以及混沌等动力学行为。通过调整平方非线性刚度系数得到了慢变外激励下相对转动系统中的对称式和不对称式fold/fold簇发行为。     

汽车转向轮摆振的稳定性及分岔行为分析

研究了减小和消除汽车转向轮摆振的方法.以三自由度前桥转向轮模型为研究对象,利用常微分方程稳定性理论和数值分析得出系统除零平衡点外其他平衡点都不会发生Hopf分岔,而且发现改变某些参数可以完全消除摆振,改变某些参数对系统摆振没有明显影响,改变某些参数还可以引起二次摆振.针对零平衡点,利用中心流形理论和规范形理论对系统进行化简并对约化方程进行分析,得到其分岔特性.进一步地,运用奇异性理论发现该系统的分岔特性在小扰动下具有很好的保持性.     

刹车系统的摩擦自激振动和控制

研究刹车系统的摩擦自激振动和控制问题。采用LuGre 模型计算摩擦力,建立了两自由度盘式刹车系统的动力学模型。通过平衡点的稳定性分析,给出Hopf 分岔失稳的临界速度。应用基于微分几何法和线性二次型最优控制相结合的方法,设计单输入单输出的非线性系统控制器,以便通过推迟系统的分岔临界速度,减少减速型刹车过程中的摩擦颤振,避免刹车啸叫。最后分析了控制器和系统参数对控制效果的影响。仿真表明,该控制器能有效的抑制刹车系统中的摩擦自激振动。     

一类时滞分数阶计算机病毒模型的Hopf分岔控制研究

研究了一类时滞分数阶计算机病毒模型Hopf分岔的控制问题。在非受控系统的第一个方程中引入周期脉冲时滞反馈控制器，采用半解析半数值的方法证明了受控系统与其线性化平均系统在一定意义下的等效性，并以此作为理论基础，采用线性化方法和分数阶Laplace变换推导受控系统发生Hopf分岔的临界值，得到系统的稳定域范围以及稳定域随控制器参数的变化情况。结果说明通过调节增益参数值，可有效的延迟系统Hopf分岔的发生。最后，通过恰当的数值模拟验证了理论分析的正确性和可行性，并对比了不同控制增益参数对系统稳定域的影响。     

球式自动平衡装置的动力学特性分析

为研究球式自动平衡装置的抑振特性,利用拉格朗日方程和牛顿定律推导出球式自动平衡装置的运动微分方程,建立平面振动模型;采用旋转坐标变换的方法将振动模型转化为自治形式方程,分析自治系统的平衡点;采用数值分岔软件AUTO完成自治系统的分岔分析,指出平衡过程中的霍夫分岔现象,并分析稳定区与不稳定区;最后采用仿真的方法验证分岔结论的正确性。     

粘弹壁板非线性颤振滞后特性分析

分析了Kelvin粘弹力模型作用下二维壁板非线性颤振系统在分岔参数连续变化时的分岔特性以及滞后特性。采用von Karman大变形理论及Kelvin粘弹阻尼模型建立二维壁板动力学方程,采用线性活塞理论建立气动力模型。利用伽辽金法将壁板颤振模型转化为常微分方程组,分析了粘弹阻尼对系统稳定性的影响,并通过数值模拟研究分岔参数连续变化时该系统的分岔特性以及分岔参数的变化方向不同时该系统的滞后行为。计算结果表明,粘弹壁板颤振系统存在静止、屈曲、极限环、浑沌等复杂的运动形式,且存在明显的滞后现象。     

一个新系统Hopf分岔极限环幅值控制

本文研究了一个新的非线性动力系统的Hopf分岔极限环幅值的控制问题.基于非线性动力系统的分岔控制理论,自主设计了一个具有普遍意义的非线性控制器.对应本系统应用具体的非线性控制器实现了Hopf分岔极限环幅值的反馈控制,同时得到了计算极限环幅值近似值的计算公式,最后数值模拟验证了本文理论分析的正确性及控制方法的有效性.     

含PID控制器的迟滞非线性控制系统的主共振及奇异性

针对含PID控制器的迟滞非线性闭环控制系统,用Backlash神经网络模型逼近系统迟滞非线性部分,建立动力学模型。研究了系统在简谐激励下的主共振,利用平均法得到了系统的分岔方程,并用奇异性理论进行了分析,得到了转迁集和分岔图。另外还研究了系统参数对开折参数和分岔参数的影响,从而为系统参数的选择提供理论指导。     

Effect of external periodic signals and electromagnetic radiation on autaptic regulation of neuronal firing

An improved Hindmarsh–Rose (HR) neuron model, where the memristor is a bridge between membrane potential and magnetic flux, can be used to investigate the effect of periodic signals on autaptic regulation of neurons under electromagnetic radiation. Based on the improved HR model driven by periodic high–low‐frequency current and electromagnetic radiation, the responses of electrical autaptic regulation with diverse high–low‐frequency signals are investigated using bifurcation analysis. It is found that the electrical modes of neurons are determined by the selecting parameters of both periodic high and low‐frequency current and electromagnetic radiation, and the Hamiltonian energy depends on the neuronal firing modes. The effects of Gaussian white noise on the membrane potential are discussed using numerical simulations. It is demonstrated that external high–low‐frequency stimulus plays a significant role in the autaptic regulation of neural firing mode, and the electrical mode of neurons can be affected by the angular frequency of both high–low‐frequency forcing current and electromagnetic radiation. The mechanism of neuronal firing regulated by high–low‐frequency signal and electromagnetic radiation discussed here could be applied to research neuronal networks and synchronisation modes.Inspec keywords: bioelectric potentials, neural nets, bifurcation, synchronisation, memristors, neurophysiology, numerical analysis, white noiseOther keywords: synchronisation modes, external periodic signals, electromagnetic radiation, improved Hindmarsh–Rose neuron model, membrane potential, periodic high–low‐frequency current, electrical autaptic regulation, diverse high–low‐frequency signals, neuronal firing modes, external high–low‐frequency stimulus, high–low‐frequency forcing current, high–low‐frequency signal, research neuronal networks     

Minimum weight design of non‐linear elastic structures with multimodal buckling constraints

It well known that multimodal instability is an event particularly relevant in structural optimization. Here, in the context of non‐linear stability theory, an exact method is developed for minimum weight design of elastic structures with multimodal buckling constraints. Given an initial design, the method generates a sequence of improved designs by determining a sequence of critical equilibrium points related to decreasing values of the structural weight. Multimodal buckling constraints are imposed without repeatedly solving an eigenvalue problem, and the difficulties related to the non‐differentiability in the common sense of state variables in multimodal critical states, are overcome by means of the Lagrange multiplier method. Further constraints impose that only the first critical equilibrium states (local maxima or bifurcation points) on the initial equilibrium path of the actual designs are taken into account. Copyright © 2002 John Wiley & Sons, Ltd.     

The Multi-Mode Rate Equations for Semiconductor Lasers with Thermal Effects

A simple mathematical model describing coupled electrical, optical and thermal effects in semiconductor lasers is introduced. The bifurcation structure of the underlying (perfect) isothermal equations is examined to acquire insight into the nature of the steady states. An infinite set of steady states is obtained at one of these bifurcation points. In the (imperfect) isothermal and thermal problems, an asymptotic analysis provides expressions for the parameter regions which characterise the stable steady states of single-mode operation. The reason that semiconductor lasers usually operate with a single dominant mode is that this corresponds to the only stable steady state. Parameter regions in which two modes share dominance are also identified.     

基于改进ESO的磁悬浮系统模型参考滑模控制

为了提高磁悬浮输送带的稳定性,减小未建模动态和未知外界干扰对磁悬浮系统控制性能的影响,基于改进的扩张状态观测器（extend state observer, ESO）技术,提出了一种模型参考滑模控制与基于改进趋近律的滑模控制相结合的控制策略。首先,对参考模型进行滑模设计,在此基础上根据磁悬浮系统的快速响应和鲁棒性要求,结合幂次趋近律和指数趋近律对传统趋近律进行改进,设计了一种基于新型趋近律的滑模控制;其次,设计了一种新的非线性函数对ESO进行改进,基于改进的ESO对系统的扰动和状态进行观测和估计,将观测结果加入新型滑模控制器以对外界干扰进行补偿,来提高新型滑模控制器的控制性能。仿真结果表明：所设计的控制策略与传统基于指数趋近律的滑模控制相比,磁悬浮系统气隙输出的超调量减小了15.15%,系统具有更高的鲁棒性;与基于改进趋近律的滑模控制方法相比,所提出的控制器可以使系统无抖振,有更好的跟踪性能。在基于改进ESO的模型参考滑模控制下,磁悬浮系统能够稳定运行,具有较好的控制性能。研究结果对磁悬浮输送机输送带的悬浮控制具有一定的参考价值。     

Lateral buckling of a cantilever beam with imperfections

Summary The stability problem of an elastic cantilever beam transversely and horizontally simultaneously end-loaded, with imperfections, as a two-parameter bifurcation problem is considered. Exact non-linear differential equations are used, which describe the buckling shape of a cantilever beam having a narrow rectangle as a cross-section. The exact solution to the linearized problem, in closed form via confluent hypergeometric functions is given. The first interaction curve, which corresponds to the critical values of the simultaneously transversely and horizontally load, is obtained. A stability analysis is based on singularity theory. The Liapunov-Schmidt method is used to generate the bifurcation equation.With 4 Figures     

一类具有食饵恐惧和避难所的反应扩散捕食模型的稳定性与 Hopf 分支

在捕食生态系统中,恐惧因子和食饵避难所都有重要的作用。为此,对一类带恐惧因子和食饵避难所的捕食-食饵反应扩散模型进行了研究。通过分析平衡点特征方程,得到了平衡点的局部渐近稳定性;将不受保护食饵比例作为分支参数,给出了正平衡点 Hopf 分支存在的条件。结果表明：避难所的存在会导致 Hopf 分支,产生空间齐次周期解。扩散的加入会产生新的Hopf分支点,产生空间非齐次周期解。这说明通过设立适当的食饵避难所或者减小捕食者的扩散,有助于物种共存。最后,利用 Matlab 进行数值模拟验证了所得的结论。     

Equilibrium and stability of interfaces between polarizable fluids: theory and computations

 A variational formulation is presented of the equilibrium and stability of interfaces between polarizable fluids in the presence of external fields. Equilibrium and stability demand minimization of an appropriate energy functional. The necessary conditions for the minimization give rise to a nonlinear and free boundary problem which is discretized and solved for the field in the fluids and the interface shape with the finite element method and Newton iteration. The sufficient conditions boil down to a generalized eigenproblem, which needs to be solved for the eigenvalues of smallest magnitude and the corresponding eigenvectors. The case studied is a rotating ferromagnetic liquid drop in an external magnetic field. Axisymmetric solutions are computed at different values of the rotational speed. They lose stability to axisymmetric disturbances at turning points and they exchange stability with non-axisymmetric solutions at bifurcation points.