用自适应脉冲微扰引导混沌系统到周期解

用自适应脉冲微扰方法控制的系统的某个系统变量作为驱动,设计了一种自适应控制器方法对两个或多个响应混沌系统进行脉冲微扰,引导这些系统从混沌运动到低周期运动,实现同时控制多个混沌系统到不同的周期态. 当选择相同的自适应控制器输入变量实施脉冲微扰时,还可控制两个或多个混沌系统达到不同的周期态同步. 通过对R?ssler混沌系统的仿真研究证实了方法的有效性. 关键词： 混沌控制 系统参量 自适应控制器 脉冲微扰 周期态同步     

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.     

Separate Polarization Modes Synchronization and Synchronization Switches between Vertical-Cavity Surface-Emitting Lasers

For vertical-cavity surface-emitting lasers (VCSELs) with polarization-rotated feedback, there exist several synchronization types such as synchronizations between total powers and synchronizations between separate polarization modes. Based on the two-mode rate equations, we study and compare numerically the performances of different synchronization types. Our results show that three synchronization types exhibit good performances when their synchronization conditions are satisfied. They are the complete synchronization between total powers, complete synchronization between x-polarized modes, and generalized synchronization between x-polarized and y-polarized modes. The former two types are sensitive to the injection rate and spontaneous emission, while the third type is contrary. Synchronization type with the best performance may switch from one to another, with changing of injection rate and spontaneous emission factor.     

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.     

Locality Hypothesis and the Speed of Light

The locality hypothesis is generally considered necessary for the study of the kinematics of non-inertial systems in special relativity. In this paper we discuss this hypothesis, showing the necessity of an improvement, in order to get a more clear understanding of the various concepts involved, like coordinate velocity and standard velocity of light. Concrete examples are shown, where these concepts are discussed.     

一类不确定混沌系统的观测器同步

基于降维观测器的方法实现了一类具有外部扰动的混沌系统的同步. 无需知道系统外部扰动项的任何信息，就可对驱动系统设计基于降维观测器的响应系统，从而实现了混沌系统的同步. 数值仿真表明该方法是有效的. 关键词： 混沌同步 混沌系统 观测器     

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.     

Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators

A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained.