共查询到20条相似文献,搜索用时 31 毫秒
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In this Letter, nonlinear dynamic and chaotic behaviors of electrostatically actuated MEMS resonators subjected to random disturbance are investigated analytically and numerically. A reduced-order model, which includes nonlinear geometric and electrostatic effects as well as random disturbance, for the resonator is developed. The necessary conditions for the rising of chaos in the stochastic system are obtained using random Melnikov approach. The results indicate that very rich random quasi-periodic and chaotic motions occur in the resonator system. The threshold of bounded noise amplitude for the onset of chaos in the resonator system increases as the noise intensity increases. 相似文献
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Nonattracting chaotic sets (chaotic saddles) are shown to be responsible for transient and intermittent dynamics in an extended system exemplified by a nonlinear regularized long-wave equation, relevant to plasma and fluid studies. As the driver amplitude is increased, the system undergoes a transition from quasiperiodicity to temporal chaos, then to spatiotemporal chaos. The resulting intermittent time series of spatiotemporal chaos displays random switching between laminar and bursty phases. We identify temporally and spatiotemporally chaotic saddles which are responsible for the laminar and bursty phases, respectively. Prior to the transition to spatiotemporal chaos, a spatiotemporally chaotic saddle is responsible for chaotic transients that mimic the dynamics of the post-transition attractor. 相似文献
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《Physics letters. A》2014,378(30-31):2142-2150
The method of recurrence plots (RPs) has been traditionally used for experimental time series analysis with no comparison with the mathematical model. This is in part because of lack of nonlinear analysis of mathematical model based on the recurrence quantification analysis (RQA) parameters. The paper provides substantial information about the mathematical and numerical analysis and synchronization of a multi-limit cycle oscillator from the RQA perspective. The recurrence quantification analysis parameters are used to discuss the birhythmic behavior of the system, as well as various bifurcations (quasi-periodicity, periodicity and chaos) in the system response. Finally, the results of the method of RPs are compared to those of phase diagrams and the problem of synchronization of limit cycle and chaotic response is discussed by the mean of cross recurrence. 相似文献
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利用替代数据法检验了摇摆条件下自然循环系统不规则复合型脉动的混沌特性, 并在此基础上进行混沌预测. 关联维数、最大Lyapunov指数等几何不变量计算结果表明不规则复合型脉动具有混沌特性, 但是由于计算结果受实验时间序列长度的限制和噪声的影响, 可能会出现错误的判断结果. 为了避免出现误判, 在提取流量脉动的非线性特征的同时, 需要用替代数据法进一步检验混沌特性是否来自于确定性的非线性系统. 本文用迭代的幅度调节Fourier 算法进行混沌检验, 在此基础上用加权一阶局域法进行混沌脉动的预测. 计算结果表明: 不规则复合型脉动是来自于确定性系统的混沌脉动, 加权一阶局域法对流量脉动进行混沌预测效果较好, 并提出动态预测方法.
关键词:
混沌时间序列
替代数据法
实时预测
两相流动不稳定性 相似文献
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The chaotic dynamics of nonlinear waves in the harmonic-forced fluid-conveying pipe in primary parametrical resonance, is explored analytically and numerically. The multiple scale method is applied to obtain an equivalent nonlinear wave equation from the complicated nonlinear governing equation describing the fluid conveyed in a pipe. With the Melnikov method, the persistence of a heteroclinic structure is shown to be satisfied and its condition is given in functional form. Similarly, for the heteroclinic orbit, using geometric analysis, a condition function of the stable manifold is derived for the orbit to return to the stable manifold from the saddle point. The persistent homoclinic structures and threshold of chaos in the Smale-horseshoe sense are obtained for the fluid-conveying pipe under both conditions, indicating how the external excitation amplitude can change substantially the global dynamics of the fluid conveyed in the pipe. A numerical approach was used to test the prediction from theory. The impact of the external excitation amplitude on the nonlinear wave in the fluid-conveying pipe was also studied from numerical simulations. Both theoretical predications and numerical simulations attest to the complex chaotic motion of fluid-conveying pipes. 相似文献
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对于离散混沌系统的最小能量控制问题,提出了一种框架性方法,该方法具有通用性.首先,设计一个二次目标函数,同时把混沌系统分解为线性部分和非线性部分两项和.然后,提出了求解非线性最优控制问题的两级算法:第一级对混沌系统中的非线性部分进行预估,以使原系统变为带有常数项的线性系统;第二级用动态规划求解一个非典型线性二次最优控制问题,并把解返回第一级,第一级根据第二级的解对非线性部分重新预估.这样通过两级间不断的信息交换,最终得到混沌系统的最优控制律.该方法不仅实现了对混沌系统的控制,而且在整个控制过程中消耗的控制能量最小.
关键词:
混沌系统
两级优化
最优控制 相似文献
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Jacobi fields on statistical manifolds of negative curvature 总被引:3,自引:0,他引:3
Two entropic dynamical models are considered. The geometric structure of the statistical manifolds underlying these models is studied. It is found that in both cases, the resulting metric manifolds are negatively curved. Moreover, the geodesics on each manifold are described by hyperbolic trajectories. A detailed analysis based on the Jacobi equation for geodesic spread is used to show that the hyperbolicity of the manifolds leads to chaotic exponential instability. A comparison between the two models leads to a relation among statistical curvature, stability of geodesics and relative entropy-like quantities. Finally, the Jacobi vector field intensity and the entropy-like quantity are suggested as possible indicators of chaoticity in the ED models due to their similarity to the conventional chaos indicators based on the Riemannian geometric approach and the Zurek-Paz criterion of linear entropy growth, respectively. 相似文献
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The plasma chaotic system is a dissipative dynamical system modeled by a parametric plasma instability arising from the interaction of the whistler and ion acoustic waves with the plasma oscillation near the lower hybrid resonance. The amplitudes of these three oscillations obey a three-dimensional system of ordinary differential equations that exhibits chaos for certain parameter values. Besides the maximal Lyapunov exponent technique, a generalized-competitive-mode (GCM) technique has been proposed to evaluate parameter values associated with chaos. A mechanical analysis has also been proposed to reveal the mechanisms underlying the different dynamical modes including chaos. In a series of comparisons between the GCM analysis and mechanical analysis, chaos for the plasma chaotic system is determined. The mechanism and causes by which the plasma chaotic system produces different dynamical behaviors are interpreted. Furthermore, using the whistler-parameter variation of the Casimir function and Casimir power for the plasma system, the generating mechanisms of the different orbital modes and the different levels of chaos are uncovered. 相似文献
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Recurrence networks are complex networks constructed from the time series of chaotic dynamical systems where the connection between two nodes is limited by the recurrence threshold. This condition makes the topology of every recurrence network unique with the degree distribution determined by the probability density variations of the representative attractor from which it is constructed. Here we numerically investigate the properties of recurrence networks from standard low-dimensional chaotic attractors using some basic network measures and show how the recurrence networks are different from random and scale-free networks. In particular, we show that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise to the time series and into the classical random graphs by increasing the range of interaction to the system size. We also highlight the effectiveness of a combined plot of characteristic path length and clustering coefficient in capturing the small changes in the network characteristics. 相似文献
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We study two-component Bose-Einstein condensates that behave
collectively as a spin system obeying the dynamics of a quantum
kicked top. Depending on the nonlinear interaction between atoms in
the classical limit, the kicked top exhibits both regular and
chaotic dynamical behavior. The quantum entanglement is physically
meaningful if the system is viewed as a bipartite system, where the
subsystem is any one of the two modes. The dynamics of the
entanglement between the two modes in this classical chaotic system
has been investigated. The chaos leads to rapid rise and saturation
of the quantum entanglement. Furthermore, the saturated values of
the entanglement fall short of its maximum. The mean entanglement
has been used to clearly display the close relation between quantum
entanglement and underlying chaos. 相似文献
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Junji Ohtsubo 《Optical Review》1999,6(1):1-15
Semiconductor laser with feedback is an excellent model for nonlinear optical system which shows chaotic dynamics. It is interesting not only from the fundamental physical study but also application standpoints of view. The dynamics of feedback induced instability and chaos, especially for optical feedback, and their applications are reviewed in this paper. The model of such a system is described by the laser rate equations. At first the dynamic behaviors of feedback induced instability and chaos in semiconductor lasers are discussed on the basis of the theory and experiments. Instability and chaos may be stabilized by the method of chaos control. Then we apply the method to suppress the noise induced by the feedback in a semiconductor laser. The synchronization of chaos between two similar systems is also an important issue in chaos applications and we discuss secure communications based on chaos synchronization. Some other examples of applications of feedback induced chaos are also described. 相似文献
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提出了一种对微弱周期信号的定量检测方法.分析混沌振子系统在大尺度周期状态下的相对稳定输出时,发现了混沌振子系统输出周期解的平均面积是一个比较稳定的几何特征量.该几何特征量与待测信号幅值之间存在比较稳定的单调递增关系.在一定的参数条件下,几何特征量精度可达到10-6V2.利用混沌系统对随机噪声信号的免疫性和对微弱周期信号的敏感性,进一步建立了微弱周期信号的定量检测方法.仿真实验表明,随着待检测幅度的增加,在保证检测精度的同时,抗噪性能也随之增强.
关键词:
混沌振子系统
大尺度周期相态
周期解的几何特征量
微弱周期信号的定量检测 相似文献
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研究一类具有同宿轨道、异宿轨道的相对转动非线性动力系统的混沌运动. 建立具有非线性刚度、非线性阻尼和外扰激励作用的一类两质量相对转动非线性动力系统的动力学方程. 利用Melnikov方法讨论了系统的全局分岔和系统进入混沌状态的可能途径,给出了系统发生混沌的必要条件,并利用最大Lyapunov指数图,分岔图,Poincare截面图和相轨迹图进一步分析了系统的混沌行为.
关键词:
相对转动
非线性动力系统
混沌
Melnikov方法 相似文献