常微分方程系统中内部激变现象的研究

应用广义胞映射图论方法研究常微分方程系统的激变.揭示了边界激变是由于混沌吸引子与 在其吸引域边界上的周期鞍碰撞产生的,在这种情况下,当系统参数通过激变临界值时,混 沌吸引子连同它的吸引域突然消失,在相空间原混沌吸引子的位置上留下了一个混沌鞍.研 究混沌吸引子大小(尺寸和形状)的突然变化,即内部激变.发现这种混沌吸引子大小的突然 变化是由于混沌吸引子与在其吸引域内部的混沌鞍碰撞产生的,这个混沌鞍是相空间非吸引 的不变集,代表内部激变后混沌吸引子新增的一部分.同时研究了这个混沌鞍的形成与演化. 给出了对永久自循环胞集和瞬态自循环胞集进行局部细化的方法. 关键词： 广义胞映射 有向图 激变 混沌鞍     

基于小波变换的混沌信号相空间重构研究

应用小波变换和非线性动力学方法研究了混沌信号在相空间中的行为，指出混沌时间序 列的小波变换实质上是在重构的相空间中，混沌吸引子向小波滤波器向量所张的空间中的投 影，与Packard等人提出的相空间重构方法本质上是一致的.实验结果表明，混沌信号经过 小波变换后，吸引子轨迹与原有轨迹具有相似的结构，同时，系统的关联维数、Kolmogorov 熵等非线性不变量仍然得到保留.这些结果表明，利用小波变换研究混沌信号是有效的. 关键词： 小波变换 相空间重构 混沌信号 脑电信号     

舰船辐射噪声超混沌现象研究

水下弱目标探测和识别一直是水声信号处理领域中研究的难点。从Lyapunov指数谱、吸引子相空间轨迹的演化、分形维数等方面，对船舶辐射噪声是否存在超混沌现象进行了研究。实验结果表明，船舶辐射噪声信号确实存在至少两个正的Lyapunov指数，即存在超混沌现象。辐射噪声吸引子在相空间中的轨迹具有多方向伸展的趋势，且不同类型目标的吸引子具有不同的分形维数。研究结果为建立精确描述辐射噪声信号的非线性模型、为水下弱目标信号探测和识别提供一定的理论依据。     

水声目标辐射噪声的低维动力学成分提取及应用

基于非线性动力学理论的水声信号相空间处理,是水声信号处理的一种新途径。实际水声信号在相空间中分析时的首要问题是降噪。本文应用局部几何投影法提取不同目标辐射噪声的低维成分,输出相图呈现出较明显的低维吸引子。在此基础上,用吸引子维数和反映动力学模型差异的交叉预测误差对样本进行了分类研究,结果表明,综合这两种分别反映几何性质和动力学性质的特征,可达到一定的分类效果。     

螺旋桨鸣音的混沌动力特性研究

利用混沌动力学方法研究螺旋桨鸣音信号时间序列,估计时间序列的相空间重构最佳参数,并提出其具有混沌动力特性,分析了系统拓扑维数的边界和生成系统所必须独立变量的个数,还计算分析了重构相空间中吸引子轨迹随时间演化的发散情况。分析计算结果表明:螺旋桨鸣音信号时间序列可以选取最佳延迟时间t_D=1、最小嵌入维数d_E=8进行相空间重构,其混沌吸引子的关联维数为5.1579、最大Lyapunov指数为0.0771,此研究结果可以为螺旋桨鸣音现象的进一步研究提供理论基础。      

倾斜油水两相流流型混沌吸引子形态周界测度分析

在两维相空间中定义了吸引子形态周界特征量（吸引子面积、长轴、短轴）,考察了吸引子周界特征量随时间延迟的变化规律.发现在吸引子展开过程的第一区域内,其吸引子周界特征量变化率具有不变性.通过对正弦信号、噪声信号和混沌信号进行仿真分析,发现采用吸引子周界特征量可以对这些不同信号进行有效分类.在采集倾斜油水两相流电导波动信号基础上,对水为连续相的倾斜油水两相流流型进行了吸引子形态周界测度分析,发现吸引子面积增长率是描述吸引子形态的不变特征量,该特征量对水为连续相的拟段塞水包油（D O/W PS）和局部逆流水包油（ 关键词： 倾斜油水两相流 流型识别 吸引子形态 周界测度     

基于数据融合的多变量相空间重构方法

针对单变量时间序列和多变量时间序列相空间重构所存在的问题,提出一种新的多变量融合的相空间重构方法. 通过Bayes估计理论,将多变量在同一相空间中进行相点的最优融合,得到了更为理想的融合相空间. 应用所提出的方法对Lorenz系统及耦合Rssler系统进行了多变量融合的相空间重构. 通过多变量重构图与单变量重构图的比较,发现基于数据融合的多变量相空间重构图包含了所有单变量相空间重构图的重要信息,使重构的相空间更加完备,较全面地反映出吸引子的全貌信息. 最后应用该方法对转子油膜涡动故障得到的多变量时间序列 关键词： 多变量时间序列 相空间重构 数据融合 Bayes估计     

横掠管束周期性充分发展对流换热的混沌分析

本文利用混沌理论分析了横掠管束周期性充分发展对流换热的非稳定性问题,即通过速度U的时间序列的重构相空间计算出关联维数D2,并通过时间序列分析了该非线性动力系统的功率谱特性。分析结果表明,本文所研究的横掠管束周期性充分发展对流换热系统在所给出的控制参数Re=937.7下出现的非稳定性问题属于混沌现象。系统的整体状态可用奇怪吸引子来描述,当延迟时间选择为5,该时间序列的重构相空间的嵌入维数增至5时,该吸引子的分维数趋于定值1.63。     

基于相空间重构理论的舰船辐射噪声非线性特性研究

以相空间重构理论为基础,用TAKENS延时法对时序序列进行相空间重构,在超维相空间中研究舰船辐射噪声的非线性特性,利用相似序列计算出空间轨迹点与其自身的重复度（RPT）参数,绘制了舰船辐射噪声重复度曲线并分析其非线性特性。结果表明,在超维相空间中,舰船辐射噪声表现出具有界于随机的高斯白噪声和确定性的LORENZ吸引子之间的空间几何特性。并且同类目标之间具有相似性,不同类目标之间具有可分性,本文所提出的方法为水声目标的非线性研究开辟了一个新的途径．     

竖壁液膜流壁面热流率对流动影响的实验研究

本文用相空间重构的方法,对竖壁薄液膜流动的液膜厚度时间序列进行了重构,并用分维数对奇怪吸引子的动力特征进行了描述,由此描述了壁面热流率对竖壁薄液膜流动特性的影响。     

The random attractor of stochastic FitzHugh-Nagumo equations in an infinite lattice with white noises

The present paper is devoted to the existence of the random attractor of stochastic FitzHugh-Nagumo equations in an infinite lattice with additive white noise. Using the Ornstein-Uhlenbeck transform, we firstly show the existence of an absorbing set, then prove that the random dynamical system is asymptotically compact. Finally, the existence of the random attractor is provided.     

Detection of determinism and randomness in time series: A method based on phase space overlap of attractors

The space overlap of an attractor reconstructed from a time series with a similarly reconstructed attractor from a random series is shown to be a sensitive measure of determinism. Results for the time series for Henon, Lorenz and Rössler systems as well as a linear stochastic signal and an experimental ECG signal are reported. The overlap increases with increasing levels of added noise, as shown in the case of Henon attractor. Further, the overlap is shown to decrease as noise is reduced in the case of the ECG signal when subjected to singular value decomposition. The scaling behaviour of the overlap with bin size affords a reliable estimate of the fractal dimension of the attractor even with limited data.     

Detection of Mechanism of Noise-Induced Synchronization between Two Identical Uncoupled Neurons

We investigate the noise-induced synchronization between two identical uncoupled Hodgkin-Huxley neurons with sinusoidal stimulations. The numerical results confirm that the value of critical noise intensity for synchronizing two systems is much less than the magnitude of mean size of the attractor in the original system, and the deterministic feature of the attractor in the original system remains unchanged. This finding is significantly different from the previous work [Phys. Rev. E 67 （2003） 027201] in which the value of the critical noise intensity for synchronizing two systems was found to be roughly equal to the magnitude of mean size of the attractor in the original system, and at this intensity, the noise swamps the qualitative structure of the attractor in the original deterministic systems to synchronize to their stochastic dynamics. Further investigation shows that the critical noise intensity for synchronizing two neurons induced by noise may be related to the structure of interspike intervals of the original systems.     

First passage time on pattern formation in a non-local Fisher population dynamics

We use stochastic dynamics to develop the patterned attractor of a non-local extended system. This is done analytically using the stochastic path perturbation approach scheme, where a theory of perturbation in the small noise parameter is introduced to analyze the random escape of the stochastic field from the unstable state. Emphasis is placed on the specific mode selection that these types of systems exhibit. Concerning the stochastic propagation of the front we have carried out Monte Carlo simulations which coincide with our theoretical predictions.     

Dynamic modes of microwave signal autogeneration in a radio photonic ring generator

Dynamic modes of microwave signal autogeneration in a radio photonic generator have been investigated. The generator is a ring circuit with a low-pass filter and microwave amplifier in its microwave path. The optical path contains an optical fiber delay line. The generator demonstrates the periodical, chaotic, and noise dynamics. It has been shown that the correlation dimensionality of the random signal attractor in the chaotic generation mode saturates with increasing phase space dimensionality. Saturation is not observed in the noise-generation mode.     

A fuzzy crisis in a Duffing-van der Pol system

A crisis in a Duffing--van del Pol system with fuzzy uncertainties is studied by means of the fuzzy generalised cell mapping (FGCM) method. A crisis happens when two fuzzy attractors collide simultaneously with a fuzzy saddle on the basin boundary as the intensity of fuzzy noise reaches a critical point. The two fuzzy attractors merge discontinuously to form one large fuzzy attractor after a crisis. A fuzzy attractor is characterized by its global topology and membership function. A fuzzy saddle with a complicated pattern of several disjoint segments is observed in phase space. It leads to a discontinuous merging crisis of fuzzy attractors. We illustrate this crisis event by considering a fixed point under additive and multiplicative fuzzy noise. Such a crisis is fuzzy noise-induced effects which cannot be seen in deterministic systems.     

Noise induced destruction of zero Lyapunov exponent in coupled chaotic systems

Recently, it has been found that noise can induce chaos and destruct the zero Lyapunov exponent in the situation where a nonchaotic attractor coexists with a nonattracting chaotic saddle, as in a periodic window [Phys. Rev. Lett. 88 (2002) 124101]. Here we report that noise can also destruct the zero Lyapunov exponent in coupled chaotic systems where there is only one attractor. Moreover, the zero Lyapunov exponent in noise free will become positive when adding noise and be proportional to the average frequency of bursting induced by noise. A physical theory and numerical simulations are presented to explain how the average frequency of bursting depends on the coupling and noise strength.     

Cross over of recurrence networks to random graphs and random geometric graphs

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.     

Character of fluctuations in deterministically thermostatted nonequilibrium systems

The application of Nose-Hoover equations of motion to analysis of stationary nonequilibrium systems-driven away from equilibrium by inherent thermostatting-is briefly discussed. The Galton board model, to which the analysis does apply, is described. Numerical simulations of this specific model suggest that the system exhibits 1/f(k) noise, with 1相似文献   

A scaling law: How an attractor's volume depends on noise level

We investigate the meaning of the dimension of a strange attractor for systems with noise. More specifically, we investigate the effect of adding noise of magnitude ε to a deterministic system with D degrees of freedom. If the attractor has dimension d and d < D, then its volume is zero. The addition of noise may be an important physical probe for experimental situations, useful for determining how much of the observed phenomena in a system is due to noise already present. When the noise is added, the attractor A_ε has positive volume. We conjecture that the generalized volume of A_ε is proportional to ε_{D ? d} for ε near 0 and show this relationship is valid in several cases. For chaotic attractors there are a variety of ways of defining d and the generalized volume definition must be chosen accordingly.