轴系扭振中的Hopf分歧分析

文中把发电机轴系扭振的分析扩展到非线性领域,并对轴系扭振中的Ｈｏｐｆ分歧现象进行了研究。     

Jeffcott平衡转子系统亚临界和超临界Hopf分叉

应用非线性动力学理论对平衡转子-轴承系统的亚临界和超临界Hopf分叉进行了分析与研究，提出了转子-轴承系统发生亚临界及超临界Hopf分叉的数值分析方法，分析了不同长径比下，转子系统的失稳转速界限曲线及发生超临界与亚临界分叉的区域．揭示了系统发生超临界Hopf分叉时，其周期解的产生是渐变的；发生亚临界Hopf分叉时，其周期解从稳定到失稳是突发性的，并不是一个渐进的过程，且长径比较小的轴承不易发生危害程度较大的亚临界分叉．     

四足机器人抗重心偏移步态优化

为解决四足机器人在其质心偏离躯干几何中心时的稳定性问题,提出了一种基于改进粒子群算法的优化方法.使用基于Hopf模型的振荡器搭建中枢模式发生器(central pattern generator,CPG)网络拓扑结构,通过对足端进行轨迹规划进而确定CPG模型相关参数,并对CPG单元间的耦合系数矩阵进行优化,使其能够输出...     

分数阶计算机病毒模型的稳定性与分岔分析

随着有线和无线通信网络的普及,计算机病毒已经成为当代信息社会的一大威胁,单纯依靠杀毒软件已经无法彻底清除病毒,而通过对其在互联网上的传播机制的分析,以及对其模型的研究,可以找到有效的防范计算机病毒的对策。因此,基于非线性动力学与分数阶系统理论,建立了一类具有饱和发生率的分数阶时滞SIQR计算机病毒模型。计算出模型的平衡点,并通过分析相应的特征方程研究了时滞对平衡点稳定性的影响。选择时滞作为分岔参数,得到了发生Hopf分岔的时滞临界值。研究发现,系统的动力学行为依赖于分岔的临界值,同时给出了系统局部稳定和产生Hopf分岔的条件。在此基础上,研究了分数阶阶次的变化对分岔阈值的影响。最后,通过数值模拟验证了理论分析的正确性。     

调度方式和负荷水平对小扰动稳定域的影响

借助WSCC 3机9节点系统研究了调度方式和负荷水平变化对小扰动稳定域的影响。首先利用边界追踪算法求解了系统在特定负荷水平下的小扰动稳定域,它是由4条Hopf分岔曲线围成的封闭区域,基于计算结果讨论了调度方式改变对小扰动稳定域的影响;然后求解了系统在不同负荷水平下的小扰动稳定域,研究了负荷水平变化时小扰动稳定域扩大、缩小、直至消失的过程,并进一步讨论了负荷水平变化对小扰动稳定域的影响。研究表明,负荷水平的变化会导致系统小扰动稳定域的组成和范围发生改变,而发电机调度方式的变化则只会改变系统当前的运行点,对小扰动稳定域的构成不产生影响。     

水轮机非线性特性作用下的水电站调速系统稳定性研究

针对水轮机非线性特性,采用Hopf分岔理论研究了水电站调速系统稳定性。即建立了考虑水轮机非线性特性的水电站调速系统数学模型,基于Hopf分岔和临界稳定判据分析了系统的稳定性,通过对比分析揭示了水轮机非线性特性对调速系统稳定性的作用机理。结果表明,考虑水轮机非线性特性的水电站调速系统Hopf分岔是超临界的,系统的稳定域位于分岔线下方。水轮机非线性特性对调速系统稳定性和调节品质的影响由水头非线性和转速非线性两种因素引起,水头非线性起主要作用,转速非线性几乎无影响。减负荷工况下水头非线性对系统稳定性有利,系统具有较好的调节品质;增负荷工况则相反。     

Global qualitative analysis of a predator–prey system with Allee effect on the prey species

In this paper, the Allee effect is incorporated into a predator–prey model with linear functional response. Compared with the predator–prey model without the Allee effect, it is found that the Allee effect of the prey species increases the extinction risk of both the prey and predator. If the Allee effect of the prey species is strong and the mortality of the predator species is relatively low, then the prey and predator cannot coexist after the predator invasion. Moreover, it is shown that the model with Allee effect undergoes the heteroclinic loop bifurcation and subcritical and supercritical Hopf bifurcations. With the brokenness of the heteroclinic loop, a stable or unstable limit cycle will appear. The Allee effect of the prey species can lead to unstable or stable periodic fluctuations. It is also found that the positive equilibrium of the model could change from stable to unstable, and then disappear when the strength of Allee effect increases continuously from zero.     

速度时滞反馈控制下磁浮系统的稳定性与Hopf分岔

The problem of time delay speed feedback in the control loop is considered here.Its effects on the linear stability and dynamic behavior of the maglev system are investigated.It is found that a Hopf bifurcation can take place when the time delay exceeds certain values.The stability condition of the maglev system with the time delay is acquired.The direction and stability of the Hopf bifurcation are determined by constructing a center manifold and by applying the normal form method.Finally,numerical simulations are performed to verify the analytical result.     

Feedback stabilization of bifurcations in multivariable nonlinear systems—Part II: Hopf bifurcations

In this paper we derive necessary and sufficient conditions of stabilizability for multi‐input nonlinear systems possessing a Hopf bifurcation with the critical mode being linearly uncontrollable, under the non‐degeneracy assumption that stability can be determined by the third order term in the normal form of the dynamics on the centre manifold. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the Hopf bifurcation of the closed‐loop system is supercritical, which is equivalent to local asymptotic stability of the system at the bifurcation point. We prove that under the non‐degeneracy conditions, stabilizability is equivalent to the existence of solutions to a third order algebraic inequality of the feedback gains. Explicit conditions for the existence of solutions to the algebraic inequality are derived, and the stabilizing feedback laws are constructed. Part of the sufficient conditions are equivalent to the rank conditions of an augmented matrix which is a generalization of the Popov–Belevitch–Hautus (PBH) rank test of controllability for linear time invariant (LTI) systems. We also apply our theory to feedback control of rotating stall in axial compression systems using bleed valve as actuators. Copyright © 2006 John Wiley & Sons, Ltd.