二次谐波系统在浑沌态下的光子统计

数值分析了调制泵浦作用下的二次谐波产生系统的浑沌动力学行为.考虑到混沌运动的遍历性,提出一种研究浑沌态光场光子统计的数值方法,即通过数值积分求解系统动力学方程估计光子数的系统平均.运用这一方法于二次谐波系统,计算了其在浑沌态下的光子统计分布,结果表明是一种超Poisson分布.     

PV型HgCdTe光电探测器中的混沌及其诊断

 对激光辐照半导体光电探测器的实验研究，发现当一束不太强的稳定连续波激光照射在PV型HgCdTe光电探测器上时，可以引起探测器出现混沌行为。利用光电探测器的光电压信号随时间变化的实验数据，通过求功率谱、计算Lyapunov指数对混沌进行了诊断。     

Pseudo-billiards

A new class of Hamiltonian dynamical systems with two degrees of freedom and kinetic energy of the form T = c₁|p₁| + c₂|p₂| (called “pseudo-billiards”) is studied. For any kind of interaction, the canonical equations can always be integrated on sequential time intervals; i.e. in principle all the trajectories can be found explicitly.

Depending on the potential, a dynamical system of this class can either be completely integrable or behave just as a usual non-integrable Hamiltonian system with two degrees of freedom: in its phase space there exist invariant tori, stochastic layers, domains of global chaos, etc. Pseudo-billiard models of both the types are considered.

If a potential of a pseudo-billiard system has critical points (equilibria), then trajectories close to these points (“loops”) can exist; they can be treated as images of self-localized objects with finite duration. Such a model (with quartic potential) is also studied.     

On a recursive method for the estimation of unknown parameters of partially observed chaotic systems

We investigate a recently proposed method for on-line parameter estimation and synchronization in chaotic systems. This novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series. It works by periodically updating the parameter of interest in a secondary system, with the same functional form as the primary one but no explicit coupling between their dynamic variables, in order to minimize a suitably defined cost function. In this paper, we review the basics of the method, and investigate its robustness and new extensions. In particular, we study the performance of the novel technique in the presence of noise (either observational, i.e., an additive contamination of the observed time series, or dynamical, i.e., a random perturbation of the system dynamics) and when there is a mismatch between the primary and secondary systems. Numerical results, including comparisons with other techniques, are presented. Finally, we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations.     

Nonlinear Time Series Analysis Since 1990:Some Personal Reflections

Abstract I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five majorareas of development. These areas include the interface between nonlinear time series analysis and chaos,thenonparametric/semiparametric approach,nonlinear state space modelling,financial time series and nonlinearmodelling of panels of time series.     

A marker method for the solution of the damped Burgers' equation

A new method for the solution of the damped Burgers' equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Investigation on chaotic motion in hysteretic non-linear suspension system with multi-frequency excitations

This paper presents the investigation on possible chaotic motion in a vehicle suspension system with hysteretic non-linearity, which is subjected to the multi-frequency excitation from road surface. The Melnikov’s function is used to derive the critical condition for the chaotic motion, and then it is investigated that the effects of parameters in non-linear damping on the chaotic field. The path from quasi-periodic to chaotic motion is found via Poincaré map and Lyapunov exponents.     

Turbulence without strange attractor

It is shown that pipe-flow turbulence consists of transients. The fractal dimensions of the dynamical process are thus all zero. Nevertheless, this is compatible with Grassberger-Procaccia analyses suggesting the existence of a high-dimensional strange attractor. The usefulness of the Grassberger-Procaccia method to detect the aging of transients is demonstrated.     

Study of a high-dimensional chaotic attractor

The nature of a very high-dimensional chaotic attractor in an infinite-dimensional phase space is examined for the purpose of studying the relationships between the physical processes occurring in the real space and the characteristics of high-dimensional attractor in the phase space. We introduce two complementary bases from which the attractor is observed, one the Lyapunov basis composed of the Lyapunov vectors and the another the Fourier basis composed of the Fourier modes. We introduce the exterior subspaces on the basis of the Lyapunov vectors and observe the chaotic motion projected onto these exteriors. It is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace goes out of the attractor. The origin of such a phenomenon is attributed to more fundamental features of our attractor, which become manifest when the attractor is observed from the Lyapunov basis. A counterpart of the phenomenon can be observed also on the Fourier basis because there is a statistical one-to-one correspondence between the Lyapunov vectors and the Fourier modes. In particular, a statistical property of the high-pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor.     

Cytochrome-c detection

Following a myocardial infarction (MI) cells die or are damaged and their contents leak into the blood circulation, resulting in elevated serum levels of various enzymes, proteins, and organic molecules. Over the past few decades, it has become standard practice to employ the detection of these elevated substances as markers for the confirmation of MIs and to monitor MI patients’ response to treatment. Although it has previously been shown that cytochrome-c, a small respiratory protein, is among those elevated, the lack of a suitable detection system has prevented its routine use in the diagnosis of MIs. We present a preliminary study in which chemiluminescence was employed to detect elevated levels of cytochrome-c in the serum of MI patients. The technique, which is specific for c-type proteins, is approx 30 times more sensitive than the traditional Coomassie blue stain and can detect as little as 0.03 μg of protein. It also has potential for diagnostic use in other diseases that are characterized by mitochondrial damage.