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。     

Chaotic laser dynamics

Chaotic emission of lasers theoretically predicted long ago has only recently been experimentally verified. A review of experiments on various laser types is given.     

Chaotic dynamics of spin-valve oscillators

Recent experimental and theoretical studies on the magnetization dynamics driven by an electric current have uncovered a number of unprecedented rich dynamic phenomena. We predict an intrinsic chaotic dynamics that has not been previously anticipated. We explicitly show that the transition to chaotic dynamics occurs through a series of period doubling bifurcations. In chaotic regime, two dramatically different power spectra, one with a well-defined peak and the other with a broadly distributed noise, are identified and explained.     

Chaotic dynamics of sea clutter

The notion that a deterministic nonlinear dynamical system (with relatively few degrees of freedom) can display aperiodic behavior has a strong bearing on sea clutter characterization: random-looking sea clutter may be the outcome of a chaotic process. This new approach envisages deterministic rules for the underlying sea clutter dynamics, in contrast to the stochastic approach where sea clutter is viewed as a random process with a large number of degrees of freedom. In this paper, we demonstrate, convincingly for the first time, the chaotic dynamics of sea clutter. We say so on the basis of results obtained using radar data collected from a series of extensive and thorough experiments, which have been carried out with ground-truthed sea clutter data sets at three different sites. The study includes correlation dimension analysis (based on the maximum likelihood principle) and Lyapunov spectrum analysis. The Lyapunov (Kaplan-Yorke) dimension, which is a byproduct of Lyapunov spectrum analysis, shows that it is indeed a good estimator of the correlation dimension. The Lyapunov spectrum also reveals that sea clutter is produced by a coupled system of nonlinear differential equations of order five or six. (c) 1997 American Institute of Physics.     

Chaotic dynamics and dielectric loss

The dielectric losses due to the chaotic dynamics in disordered heterogeneous systems of the type of statistical mixtures with a chaotic distribution of the components having the real permittivities of opposite signs are investigated. The specific features observed in the behavior of these systems in the vicinity of the percolation threshold and far away from it are analyzed, and a comparison with the hierarchical dual media obtained by the mixing procedure is performed.     

Chaotic dynamics on large networks

Many systems in nature are governed by a large number of agents that interact nonlinearly through complex feedback loops. When the networks are sufficiently large and interconnected, they typically exhibit self-organization and chaos. This paper examines the prevalence and degree of chaos on large unweighted recurrent networks of ordinary differential equations with sigmoidal nonlinearities and unit coupling. The largest Lyapunov exponent is used as the signature and measure of the chaos, and the study includes the effects of damping, asymmetries in the distribution of coupling strengths, network symmetry, and sparseness of connections. Minimum conditions and optimal network architectures are determined for the existence of chaos. The results have implications for the design of social and other networks in the real world in which weak chaos is deemed desirable or as a way of understanding why certain networks might exist on "the edge of chaos."     

Chaotic dynamics in two-dimensional superionics

A simple model neglecting the internal friction is studied as an attempt to achieve a better understanding of both temperature and stoichiometry dependence of the low-frequency Raman lines. The model accounts for the particular structure as well as for the ion hoppings. A new mechanism for the specific behaviour of the phonon modes in β-aluminas is suggested. Upon traversing a certain critical value of the temperature, the potential barrier variations results in a completely new individual ion motion: An infinite cascade of bifurcations leads to destruction of the harmonic oscillators and a broad band noise in the spectral density is established.     

Chaotic dynamics of high-order neural networks

The dynamics of an extremely diluted neural network with high-order synapses acting as corrections to the Hopfield model is investigated. The learning rules for the high-order connections contain mixing of memories, different from all the previous generalizations of the Hopfield model. The dynamics may display fixed points or periodic and chaotic orbits, depending on the weight of the high-order connections , the noise levelT, and the network load, defined as the ratio between the number of stored patterns and the mean connectivity per neuron, =P/C. As in the related fully connected case, there is an optimal value of the weight that improves the storage capacity of the system (the capacity diverges).     

Chaotic dynamics of a whirling pendulum

A physical system is considered consisting of a rigid frame which is free to rotate about a vertical axis and to which is attached a planar simple pendulum. This system has “one and a half” degrees of freedom due to the fact that the frame and pendulum may freely rotate about the vertical axis, i.e., conservation of angular momentum holds for the “ideal”, or unperturbed, system. Using a Hamiltonian formulation we reduce the unperturbed equations of motion to a conservative planar system in which the constant angular momentum plays the role of a parameter. This system is shown to possess one or two sets of homoclinic motions depending on the level of the angular momentum. When this system is perturbed by external excitations and dissipative forces these homoclinic motions can break into homoclinic tangles providing the conditions for chaotic motions of the horseshoe type to exist. The criteria for this to occur can be formulated using a variation of Melnikov's method developed for slowly varying oscillators [1, 2]. For the present problem, the angular momentum becomes a slowly varying parameter upon addition of the disturbances. These ideas are used to rigorously prove the existence of chaotic motions for this system and to compute, to first order, global bifurcation parameter conditions. Since two types of homoclinic motions can occur, two different chaotic modes of motion can result and physical interpretations of these motions are given. In addition, a limiting case is considered in which the system becomes a single degree of freedom oscillator with parametric excitation.     

Chaotic dynamics of semiconductor microring lasers

The complexity and dynamics of chaotic attractors generated in an InGaAsP-InP microring laser are calculated and evaluated by using a multimode rate equation model. Chaos originates from the continuous mutual injections from each mode to the other because of the bus waveguide's residual reflectivity at high values of the injection current. The data analysis of the filtered output power reveals high-dimensional chaos, and phase-dependent behavior is demonstrated.     

Chaotic dynamics of a bouncing ball

A detailed study of a mapping on a two-dimensional manifold is made. The mapping describes a system subject to periodic forcing, in particular an imperfectly elastic ball bouncing on a vibrating platform. Quasiperiodic motion on a one-dimensional manifold is proven, and observed numerically, at low forcing, while at higher forcing Smale horseshoes are present. We examine the evolution of the attracting set with changing parameter. Spatial structure is oganised by fixed points of the mapping and sudden changes occur by crises. A new type of chaos, in which a trajectory alternates between two distinct chaotic regions, is described and explained in terms of manifold collisions. Throughout we are concerned to examine the behaviour of Lyapunov exponents. Typical behaviour of Lyapunov exponents in the quasiperiodic regime under the influence of external noise is discussed. At higher forcing a certain symmetry of the attractor allows an analytic expression for the exponents to be given.     

Chaotic dynamics of simple vibrational systems

This study discusses the development of a technique for analysis of the dynamical regimes of complex mechanical systems consisting of a rotor motor coupled to a system with multi-degrees-of-freedom. To understand the possible qualitatively different dynamical regimes in such systems, a simple mechanical system is considered of the “rotator-oscillator” type with a finite power source. This system has four degrees-of-freedom and is defined in four-dimensional cylindrical phase space with 12 parameters. Near the main resonance the original system is reduced to the Lorenz system with four parameters defined in a three-dimensional Cartesian phase space. This is done with the help of a special change of variables, parameters, and employing an averaging method. Studying the latter system, the existence of one of the chaotic attractors, namely of Lorenz attractor is established. Also established is the Feigenbaum attractor and the alternation. Chaotic limit sets define chaotic behavior of the instantaneous frequency of rotation of the asynchronous motor. The Poincare mappings are presented to show the correspondence of the original 4 dof and averaged 3 dof systems. The qualitative rotational characteristics for different values of the system parameters are obtained. In particular, the system can possess normal Sommerfeld effect, doubled Sommerfeld effect and a so-called scattering of the torque curve. The scattering of the torque curve (which is a known effect in micro-electronics) is likely to be a new effect in mechanics. In contrast to the Sommerfeld effect, when frequency or amplitude jumps occur instantaneously (once the unstable point of the characteristic is reached), the jump to a next stable point may take a certain time, even infinite one. Such chaotic mistuning of the motor frequency would result in random vibrations leading to system wear and damage.     

Chaotic complex dynamics and Newton's method

We consider one-parameter families of Julia sets arising from Newton's method in the complex domain. We show the existence of bifurcation points where zeros coalesce or change from attractors to repellors, and points where chaotic behavior occurs.     

Chaotic behavior in transverse-mode laser dynamics

We analyze chaotic behavior found in numerical simulations of the transverse pattern dynamics of a laser demonstrating that in some cases chaos originates in phase dynamics and is of low dimension. Investigations of both a Ginzburg-Landau equation for the complex field amplitude of the laser output and a Kuramoto-Sivashinsky-type equation for only the phase of that complex field equation find the same behavior. Both equations can be expanded in terms of spatial modes and in the chaotic regime the behavior of the modal amplitudes seems relatively independent. However, the fluctuations of the modal amplitudes are sufficiently correlated so that the spatiotemporal dynamics is a form of low dimensional chaos rather than a more complex turbulent behavior or even one that might merit the term spatiotemporal chaos.     

Chaotic dynamics in optimal monetary policy

There is by now a large consensus in modern monetary policy. This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy as developed by, e.g., Goodfriend and King [NBER Macroeconomics Annual 1997 edited by B. Bernanke and J. Rotemberg (Cambridge, Mass.: MIT Press, 1997), pp. 231–282], Clarida et al. [J. Econ. Lit. 37, 1661 (1999)], Svensson [J. Mon. Econ. 43, 607 (1999)] and Woodford [Interest and Prices: Foundations of a Theory of Monetary Policy (Princeton, New Jersey, Princeton University Press, 2003)]. In this paper we extend the standard optimal monetary policy model by introducing nonlinearity into the Phillips curve. Under the specific form of nonlinearity proposed in our paper (which allows for convexity and concavity and secures closed form solutions), we show that the introduction of a nonlinear Phillips curve into the structure of the standard model in a discrete time and deterministic framework produces radical changes to the major conclusions regarding stability and the efficiency of monetary policy. We emphasize the following main results: (i) instead of a unique fixed point we end up with multiple equilibria; (ii) instead of saddle-path stability, for different sets of parameter values we may have saddle stability, totally unstable equilibria and chaotic attractors; (iii) for certain degrees of convexity and/or concavity of the Phillips curve, where endogenous fluctuations arise, one is able to encounter various results that seem intuitively correct. Firstly, when the Central Bank pays attention essentially to inflation targeting, the inflation rate has a lower mean and is less volatile; secondly, when the degree of price stickiness is high, the inflation rate displays a larger mean and higher volatility (but this is sensitive to the values given to the parameters of the model); and thirdly, the higher the target value of the output gap chosen by the Central Bank, the higher is the inflation rate and its volatility.     

Chaotic properties of systems with Markov dynamics

We present a general approach for computing the dynamic partition function of a continuous-time Markov process. The Ruelle topological pressure is identified with the large deviation function of a physical observable. We construct for the first time a corresponding finite Kolmogorov-Sinai entropy for these processes. Then, as an example, the latter is computed for a symmetric exclusion process. We further present the first exact calculation of the topological pressure for an N-body stochastic interacting system, namely, an infinite-range Ising model endowed with spin-flip dynamics. Expressions for the Kolmogorov-Sinai and the topological entropies follow.     

Chaotic dynamics of the fractional Lorenz system

In this Letter we introduce a generalization of the Lorenz dynamical system using fractional derivatives. Thus, the system can have an effective noninteger dimension Sigma defined as a sum of the orders of all involved derivatives. We found that the system with Sigma<3 can exhibit chaotic behavior. A striking finding is that there is a critical value of the effective dimension Sigma(cr), under which the system undergoes a transition from chaotic dynamics to regular one.     

Chaotic dynamics in piezoelectrically active statistical mixtures

The dielectric losses and the piezoelectric effect are investigated in disordered heterogeneous systems of the type of piezoelectrically active statistical mixtures with a random distribution of components having real permittivities of different signs. It is demonstrated that the permittivities and the piezoelectric constants correlate with the chaotic dynamics. The specific features of the behavior of these systems in the vicinity of the percolation threshold and far away from it are analyzed.     

Chaotic dynamics,fluctuations, nonequilibrium ensembles

The ideas and the conceptual steps leading from the ergodic hypothesis for equilibrium statistical mechanics to the chaotic hypothesis for equilibrium and nonequilibrium statistical mechanics are illustrated. The fluctuation theorem linear law and universal slope prediction for reversible systems is briefly derived. Applications to fluids are briefly alluded to. (c) 1998 American Institute of Physics.