平行电磁场中锂原子自电离的半经典分析

采用包含组合回归的扩展的闭合轨道理论计算了平行电磁场中锂原子依赖于时间的自电离谱,并用半经典的方法解释了电离过程中的混沌现象.讨论了电离电子逃逸时间谱分形结构中隐含的各韵律段的电离轨迹,并得到了轨迹的一般规律,其中特别关注由核散射产生的特殊的逃逸轨迹的性质.具体研究了磁场对锂原子自电离混沌脉冲阵列中电子逃逸轨道和逃逸时间谱的影响.结果发现随着外加磁场的增大,电离脉冲越来越复杂,混沌现象也越明显.这显示了逃逸轨道对初始条件的敏感依赖性.     

利用主动-被动法实现Bragg声光双稳系统的混沌同步

将主动-被动同步法运用于离散混沌系统,对混沌同步问题进行了研究.根据Lyapunov稳定性理论,对系统进行一般分解,实现了离散系统的混沌同步,以Bragg声光双稳系统为例,验证了这种方法的有效性.仿真模拟结果表明,控制后的两个初始条件不同的Bragg声光双稳系统误差变量很快平稳地趋于零,说明这种同步方法是快速有效的.这种方法可以应用到任意的两个初始条件不同的离散和连续混沌系统,具有一定的普适性.     

对量子混沌系统的一般认识

混沌运动对于一个经典的可积系统,存在着与系统自由数相等数目的运动积分。这样的系统在给定初始条件后,随时间的演变运动状态仅占据相空间的一部分,且通常具有周期性的特点,轨道分布在n 维环面上,不同的初始条件定义不同的环面,这样的运动是规则运动。另一方面,对规则运动,可以通过解运动方程给出运动的全部规律。     

非周期力在混沌控制中的双重功效

探讨了非周期力（有界噪声或混沌驱动力）在非线性动力系统混沌控制中的影响.以一类典型的含有五次非线性项的Duffing-van der Pol系统为范例,通过对系统的轨道、最大Lyapunov指数、功率谱幅值及Poincar截面的分析,发现适当幅值的有界噪声或混沌信号,一方面可以消除系统对初始条件的敏感依赖性,抑制系统的混沌行为,将系统的混沌吸引子转化为奇怪非混沌吸引子;另一方面也可以诱导系统的混沌行为,将系统的周期吸引子转化为混沌吸引子.从而揭示了非周期力在混沌控制中的双重功效：抑制混沌和诱导混沌. 关键词： 混沌控制 有界噪声 混沌驱动力     

基于引力场理论的混沌同步

通过引入分布引力场,将混沌系统的同步问题等效为引力场中系统运行轨道一致问题,从而实现更多不同动力学混沌系统的同步.通过将混沌系统之间的耦合度定义为速度,因其与运动方程无关,从而有别于常见的混沌同步控制项,具有较强通用性.基于轨道逼近导出引力场中多个混沌系统同步的条件,给出同步轨道方程.数值仿真实验说明了该方法的有效性.     

临界阻尼和过阻尼振动札记

本文讨论了在不同初始条件下临界阻尼和过阻尼振动的位移—时间关系和相轨道,给出了质点在不同情况下趋于平衡所需要的时间与初始条件的关系,指出了一些教材中在这个问题论述上的局限与不足.     

用驱动参量法实现混沌系统的同步

提出了通过外部混沌信号驱动两个混沌系统的某个参量并导致其同步的方法,以logistic映象和Lorenz系统这两个典型混沌系统为例,数值地研究了这种混沌同步方法.模拟结果表明,当被驱动参量的变化范围足够大时,两个或多个混沌系统在新的动力学的基础上达到完全同步.特别强调指出的是,观察到了两个Lorenz系统依赖于初始条件的不同的同步态 关键词： 混沌 同步 驱动参量法 反向同步     

电场中里德伯原子动力学性质的半经典理论研究

利用闭合轨道理论和Poincaré截面两种方法研究了鞍点附近电场中高里德伯态Li原子的动力学性质.由于原子实的作用,体系是混沌的,闭合轨道和周期轨道在混沌体系中并存,但二者在Poincaré截面上的反映是不同的.讨论了两种半经典理论在研究混沌体系时的联系,得到了仅靠闭合轨道理论得不到的信息. 关键词： Poincaré截面 回归谱 Stark效应     

一个一维周期驱动哈密顿系统的实例及混沌控制

提出一种新的周期驱动非线性不可积哈密顿系统模型,并对其特性进行了讨论.通过简单的非反馈控制装置对这一系统进行混沌控制,将其混沌轨道分别控制在周期,准周期及指定混沌轨道上.与以往的控制方法不同的是,控制项仅是一结构简单、可调节的限位装置.为保守系统混沌控制的实际应用提供可供选择的途径     

玻色-爱因斯坦凝聚中的混沌反控制

提出一种实现玻色-爱因斯坦凝聚中的混沌反控制方法——周期信号驱动法.数值模拟结果表明,用小的周期信号控制系统,采用恰当的调制相位和强度,只要满足系统的最大Lyapunov指数大于零即可实现不同的混沌轨道重构.调制相位在混沌轨道重构中起了很重要的作用. 关键词： 玻色-爱因斯坦凝聚 混沌反控制 小周期信号 Lyapunov指数     

Finite-Time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics

In an earlier work we have shown the global (for all initial data and all time) well-posedness of strong solutions to the three-dimensional viscous primitive equations of large scale oceanic and atmospheric dynamics. In this paper we show that for certain class of initial data the corresponding smooth solutions of the inviscid (non-viscous) primitive equations, if they exist, they blow up in finite time. Specifically, we consider the three-dimensional inviscid primitive equations in a three-dimensional infinite horizontal channel, subject to periodic boundary conditions in the horizontal directions, and with no-normal flow boundary conditions on the solid, top and bottom boundaries. For certain class of initial data we reduce this system into the two-dimensional system of primitive equations in an infinite horizontal strip with the same type of boundary conditions; and then we show that for specific sub-class of initial data the corresponding smooth solutions of the reduced inviscid two-dimensional system develop singularities in finite time.     

Development of stochastic oscillations in a one-dimensional dynamical system described by the Korteweg-de Vries equation

The behavior of the solution of the Korteweg-de Vries equation for large-scale oscillating periodic initial conditions prescribed on the entire x axis is considered. It is shown that the structure of small-scale oscillations arising in a Korteweg-de Vries system as t→∞ loses its dynamical properties as a consequence of phase mixing. This process can be called the generation of soliton turbulence. The infinite system of interacting solitons with random phases developing under these conditions leads to oscillations having a stochastic character. Such a system can be described using the terms applied to a continuous random process, the probability density and correlation function. It is shown that for this it suffices to determine from the prescribed initial conditions amplitude distribution function of the solitons and their mean spatial density. The limiting stochastic characteristics of the mixed state for problems with initial data in the form of an infinite sequence of isolated small-scale pulses are found. Also, the problem of stochastic mixing under arbitrary initial conditions in the dispersionless limit (the Hopf equation) is completely solved. Zh. éksp. Teor. Fiz. 115, 333–360 (January 1999)     

Dynamic features of stimulated raman atomic-molecular conversion in a mixture of two bose gases with the formation of bose condensates of heteronuclear molecules

Based on the mean-field approximation, a system of nonlinear differential equations is obtained which describes the dynamics of atomic-molecular conversion induced by two resonance Raman laser pulses. The obtained integrals of motion allow one to reduce the problem to one evolution equation for the density of molecules. The solutions of this equation show that different time evolution regimes of the system are possible, depending on the initial conditions: the periodic and aperiodic regimes and the rest. The dependences of the period and amplitude on the initial density of particles and the initial phase difference are studied in detail. The possibility of the phase control of the system dynamics is proved.     

级联混沌及其动力学特性研究

初值敏感性是混沌的本质,混沌的随机性来源于其对初始条件的高度敏感性,而Lyapunov指数又是这种初值敏感性的一种度量.本文的研究发现,混沌系统的级联可明显提高级联混沌的Lyapunov指数,改善其动力学特性.因此,本文研究了混沌系统的级联和级联混沌对动力学特性的影响,提出了混沌系统级联的定义及条件,从理论上证明了级联混沌的Lyapunov指数为各个级联子系统Lyapunov指数之和;适当的级联可增加系统参数、扩展混沌映射和满映射的参数区间,由此可提高混沌映射的初值敏感性和混沌伪随机序列的安全性.以Logistic映射、Cubic映射和Tent映射为例,研究了Logistic-Logistic级联、Logistic-Cubic级联和Logistic-Tent级联的动力学特性,验证了级联混沌动力学性能的改善.级联混沌可作为伪随机数发生器的随机信号源,用以产生初值敏感性更高、安全性更好的伪随机序列.     

Study of squeezing in spin clusters

The conditions under which spin squeezing occurs in an asymmetric chain of spins are discussed. The time evolution of the system is calculated for different initial conditions. The effects of the use of spin coherent states to model the initial condition are analyzed.     

基于多重耦合映像格子的信号初值恢复研究

利用耦合映像格子恢复信号初值是信号处理研究中一个重要的问题.耦合映像格子具有混沌系统的初值敏感性，当初值受到噪声污染时将会影响到系统对其的恢复.提出了一种由多个一维耦合映像格子系统并列耦合而成的多重耦合映像格子系统，通过将多个一维系统耦合，使因受到噪声干扰而趋向于指数分离的混沌轨道相互靠近，以达到抑制噪声的目的.数值仿真表明，该系统具有较强的抗噪声能力和较高的鲁棒性.在耦合系数选取适当的情况下，即使初始信号受到噪声干扰，该多重耦合系统仍然能够很好地恢复信号初值的统计特性，且对单个初值的恢复情况及与初始信号 关键词： 耦合映像格子 恢复信号的统计特性 多重耦合     

Hamiltonian approach to the dynamics of a chemostat

Based on the Hamiltonian approach to an analysis of the system of Monod equations describing the chemostat dynamics, their partial analytical solution is found for a certain class of initial conditions. It is shown that this class of initial conditions can be easily realized in microbiological practice, and the solution obtained is generally described by the attractor of the system trajectories. A methodical approach, which allows the given Hamiltonian formalism to be used to analyze the kinetics of growth of microorganisms in the chemostat, is developed and experimentally checked. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–53, July, 2000.