利用驻波实验研究混沌现象

利用驻波实验演示了混沌现象,并对其进行了理论分析和计算机仿真研究.仿真结果与实验结果都表明:当连接点接近驻波波节处时,振动系统处于混沌运动状态;而当连接点接近驻波波腹处时,系统处于稳定驻波运动状态.     

A locally computed suboptimal control strategy for a class of interconnected systems

In this paper, a locally computed suboptimal control strategy for a class of interconnected systems is introduced. First, optimal statefeedback control equations are derived for a finite-horizon quadratic cost. Then, the control for each subsystem is separated into two portions. The first portion stabilizes the isolated subsystem, and the second portion corresponds to the interactions. To achieve a locally calculable control, an approximation to the optimal control equations is introduced, and two iterative suboptimal control algorithms are developed. In the first algorithm, the initial conditions of subsystems are assumed to be known; in the second algorithm, this information is replaced by statistical distributions. The orders of errors in the iterations of the algorithm and in the suboptimality are given in terms of interconnections. An example with comparisons is also included to show the performance of the approach.     

一类非线性常微分方程振荡解的渐近表示

在本文中,我们讨论了非线性常微分方程y"=a0|x|αy3 a1|x|βy2 α2|x|γy α3|x|δ振荡解的渐近表示．在这个方程中将α0,α,α1,β,α2,γ,α3,δ分别换成0,0,6,0,0,0,sgn(x),1就是著名的第一类Painleve方程,而将α0,α,α1,β,α2,γ,α3,δ分别换成2,0,0,0,sgn(x),1,α0,就是著名的第二类Painleve方程．当α0,α,α1,β,α2,γ,α3,δ分别换成-β/3γ,0,0,0,1/γ,1,α,0时,可用于组合KdV方程孤立子解的化简．     

Chaotic oscillations and noise transformations in a simple dissipative system with delayed feedback

We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties.     

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 telescope illumination system for a wide-field endoscope

Endoscopic illumination systems conduct light down a built-in fibre-optic bundle to illuminate the object. Many modern endoscopes employ wide-field imaging optical systems and therefore require an illuminating beam of large divergence. This is commonly provided by placing a strong diverging lens at the far end of the fibre bundle, but it results in a poor uniformity of illumination in the object space. This paper describes the design of a telescopic illumination system to overcome this problem.     

多元线性回归应用于近代物理实验

本文介绍非线性方程转化直线性方程和多元线性回归法来分析近代物理实验中塞曼效应分裂干涉圆环多处选点测量的处理过程。     

时滞差分系统基于两种度量的稳定性分析

本文建立了一些关于时滞差分系统（h0,h）稳定性（一致稳定性，渐近稳定性，一致渐近稳定性）的判定准则。在所得到的定理中，去除了△V为常负的限制，特别地，△V甚至可以恒为正，从而大大改进了已有结果，并更加便于应用。     

Demonstration of Soliton Solutions of DNLS Equation by Liouville Theorem

In the inverse scattering transform (IST), the reflectionless Jost solutions are combined by their analytic properties in the complex spectrum parameter plane, and then can be shown to satisfy the two Lax equations indeed by Liouville theorem. So the corresponding soliton solutions certainly satisfy the nonlinear equation by compatibility condition. Especially the multi-soliton solutions of DNLS equation can be demonstrated in this way. PACS Numbers: 05.45.Yv, 02.30.-f, 11.10.Ef