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1.
van der Pol-Duffing时滞系统的稳定性和Hopf分岔   总被引:9,自引:1,他引:8  
徐鉴  陆启韶  王乘 《力学学报》2000,32(1):112-116
研究了具有三次项的van der Pol-Duffing非线性时滞系统的稳定性和Hopf分岔,分析了当线性化特征方程随两参数(时滞量和增益系数)变化时特征根的分布;证明了Hopf分岔的存在性,通过构造中心流形并且使用范式方法给出的Hopf分岔的方向以及周期解的稳定性,讨论时滞量对该系统的Hopf分岔的影响。  相似文献   

2.
时滞Lienard非线性系统的Hopf分岔   总被引:3,自引:0,他引:3  
本文研究了Lienard非线性时滞系统的线性稳定性和Hopf分岔,考究了特征方程随两参数变化时根的分布,应用中心流形和范式分析失去线性稳定性出现的Hopf分岔及其稳定性。  相似文献   

3.
机床动力学中含时滞颤振系统的分岔问题的研究   总被引:2,自引:0,他引:2  
本文针对机床动力学中一种典型的非线性完全再生颤振模型,分析证明了这种二阶有限时滞微分方程的Hopf分岔的存在条件,推导出分岔周期解的表达式,并结合工程实例,给出了产生分岔的参数范围。  相似文献   

4.
非线性模态构造方法与机电耦合系统Hopf分岔   总被引:2,自引:0,他引:2  
大型汽轮发电机组轴系与电网耦合次同步谐振(SSR)现象是在某种参数条件下机电耦合系统产生Hopf分岔的结果。在文献[1]中,作者提出了分析这种系统Hopf分岔的非线性模态方法,得出了在固定参数下分岔解的结果。本文针对高维非线性动力系统(包括奇数维),提出新的非线性模态构造方法,并给出了机电耦合次同步振荡系统在辅助参数变化条件下分岔解的的变化规律。  相似文献   

5.
本文研究了Hopf分岔的分岔方向控制问题,提出子非线性信射系统HHopf分岔方向控制的频域方法,获得了分岔方向可控性的充分条件,并将Hopf分岔方向控制应用osaler系统的控制。  相似文献   

6.
本文采用Muszynska密封力模型分析单圆盘转子--密封系统的低频自激振动:研究了系统的线性化稳定性与系统参数的关系;利用Porre的代数判据确定了平衡转子系统Hopf分岔解的发岔方向和稳定性;数值计算验了理论分析的结果。  相似文献   

7.
黄羽  徐鉴 《力学季刊》2005,26(4):669-672
众所周知,平面自治系统即使具有光滑非线性存在,系统也不会出现复杂的动力学行为。本文研究这样的系统存在时滞时,时滞量对系统的动力学行为的影响。通过对一个平面自治非线性系统引入时滞反馈,得到数学模型。利用泛函分析和平均法建立系统平衡态随时滞量变化的失稳机理,研究表明:时滞量平面自治系统动力学行为的影响是本质的.时滞量不但可以使系统出现Hopf分岔,产生周期振动。而且还可以使系统出现多稳态的周期运动或周期吸引子,这些共存的吸引子相碰是导致系统复杂的动力学行为,包括概周期和混沌运动。  相似文献   

8.
本文对挤压阴尼器-滑动轴承-柔性转子系统的稳定性及分岔特性进行了理论分析,首先讨论了系统平衡位置的稳定性及共Hopf分岔,然后讨论了不平衡响应的稳定性及分岔。分析表明:在一定参数条件下,系统的稳态响应将发生倍周期分岔、二次Hopf分岔及鞍-结分岔。  相似文献   

9.
具有非线性滞回特性的振动系统的稳定性及贫岔行为研究   总被引:1,自引:0,他引:1  
本文研究了具有非线性滞回特性的振动系统的稳定性及分岔行为,讨论了系统微分方程的非临界情形,分析了系统具有单零和一对纯虚数特征值的分岔行为,得到了滞回系统的具有7阶精度的中心流形及Hopf分岔必要条件。  相似文献   

10.
本文采用Muszynska密封力模型分析单圆盘转子--密封系统的低频自激振动。文(1)研究了平衡转子的稳定性和分岔,本文研究不平衡转子在临界平衡点附近自激振动(周期扰动Hopf分岔)的亚谐共振,给出了不同参数条件下的振动性态,为识别转子的亚谐共振故障及预防提供了一些新理论依据。  相似文献   

11.
This paper investigates the dynamical behaviors for a four-dimensional energy resource system with time delay, especially in terms of equilibria analyses and Hopf bifurcation analysis. By setting the time delay as a bifurcation parameter, it is shown that Hopf bifurcation would occur when the time delay exceeds a sequence of critical values. Furthermore, the stability and direction of the Hopf bifurcation are determined via the normal form theory and the center manifold reduction theorem. Numerical examples are given in the end of the paper to verify the theoretical results.  相似文献   

12.
In this paper, the dynamics of a pair of van der Pol oscillators with delayed velocity coupling is studied by taking the time delay as a bifurcation parameter. We first investigate the stability of the zero equilibrium and the existence of Hopf bifurcations induced by delay, and then study the direction and stability of the Hopf bifurcations. Then by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups, we investigate the spatio-temporal patterns of Hopf bifurcating periodic oscillations. We find that there are different in-phase and anti-phase patterns as the coupling time delay is increased. The analytical theory is supported by numerical simulations, which show good agreement with the theory.  相似文献   

13.
时滞动力系统的稳定性与分岔:从理论走向应用   总被引:1,自引:0,他引:1  
本文综述了近年来时滞动力系统稳定性与分岔方面的研究进展, 重点阐述了作者及其团队在稳定性分析、Hopf分岔计算、利用时滞改善系统稳定性等方面的一些理论和方法研究结果, 介绍了时滞对颤振主动控制系统、不稳定系统镇定、网络系统的影响等方面的研究. 基于研究体会, 对进一步的研究提出了若干展望.  相似文献   

14.
We study the appearance and stability of spatiotemporal periodic patterns like phase-locked oscillations, mirror-reflecting waves, standing waves, in-phase or antiphase oscillations, and coexistence of multiple patterns, in a ring of bidirectionally delay coupled oscillators. Hopf bifurcation, Hopf–Hopf bifurcation, and the equivariant Hopf bifurcation are studied in the viewpoint of normal forms obtained by using the method of multiple scales which is a kind of perturbation technique, thus a clear bifurcation scenario is depicted. We find time delay significantly affects the dynamics and induces rich spatiotemporal patterns. With the help of the unfolding system near Hopf–Hopf bifurcation, it is confirmed in some regions two kinds of stable oscillations may coexist. These phenomena are shown for the delay coupled limit cycle oscillators as well as for the delay coupled chaotic Hindmarsh–Rose neurons.  相似文献   

15.
非自治时滞反馈控制系统的周期解分岔和混沌   总被引:9,自引:0,他引:9  
徐鉴  陆启韶 《力学学报》2003,35(4):443-451
研究时滞反馈控制对具有周期外激励非线性系统复杂性的影响机理,研究对应的线性平衡态失稳的临界边界,将时滞非线性控制方程化为泛函微分方程,给出由Hopf分岔产生的周期解的解析形式.通过分析周期解的稳定性得到周期解的失稳区域,使用数值分析观察到时滞在该区域可以导致系统出现倍周期运动、锁相运动、概周期运动和混沌运动以及两条通向混沌的道路:倍周期分岔和环面破裂.其结果表明,时滞在控制系统中可以作为控制和产生系统的复杂运动的控制“开关”.  相似文献   

16.
A simple delayed neural network model with three neurons is considered. By constructing suitable Lyapunov functions, we obtain sufficient delay-dependent criteria to ensure global asymptotical stability of the equilibrium of a tri-neuron network with single time delay. Local stability of the model is investigated by analyzing the associated characteristic equation. It is found that Hopf bifurcation occurs when the time delay varies and passes a sequence of critical values. The stability and direction of bifurcating periodic solution are determined by applying the normal form theory and the center manifold theorem. If the associated characteristic equation of linearized system evaluated at a critical point involves a repeated pair of pure imaginary eigenvalues, then the double Hopf bifurcation is also found to occur in this model. Our main attention will be paid to the double Hopf bifurcation associated with resonance. Some Numerical examples are finally given for justifying the theoretical results.  相似文献   

17.
In this paper, we aim to investigate the dynamics of a system of Van der Pol–Duffing oscillators with delay coupling. First, taking the time delay as a bifurcation parameter, the stability of the equilibrium, and the existence of Hopf bifurcation are investigated. Then using the center manifold reduction technique and normal form theory, we give the direction of the Hopf bifurcation. And then by means of the symmetric bifurcation theory for delay differential equations and the representation theory of groups, we claim the bifurcation periodic solution induced by time delay is antiphase locked oscillation. Finally, at the end of the paper, numerical simulations are carried out to support our theoretical analysis.  相似文献   

18.
The dynamics of a diffusive predator–prey model with time delay and Michaelis–Menten-type harvesting subject to Neumann boundary condition is considered. Turing instability and Hopf bifurcation at positive equilibrium for the system without delay are investigated. Time delay-induced instability and Hopf bifurcation are also discussed. By the theory of normal form and center manifold, conditions for determining the bifurcation direction and the stability of bifurcating periodic solution are derived. Some numerical simulations are carried out for illustrating the theoretical results.  相似文献   

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