非线性光学 非线性光学器件

O437 2005042695 状态反馈控制声光双稳系统的倍周期分岔和混沌=Con- trol of period-doubling bifurcation and chaos in acousto-op- tical bistable system by the feedback of states[刊,中]／吕翎(辽宁师范大学物理系,辽宁,大连(116029)),杜增…／／光子学报,-2004,33(11),-1401-1404 设计了一种动力学状态反馈(DSF)方法控制非线性混沌系统。介绍了DSF方法的控制原理,并用此方法控制声光双稳(AOB)系统的混沌,以此验证其有效性。仿真模拟显示,通过选择恰当的控制参数,有效地实现了声光双稳     

间隙线性反馈控制混沌

提出了两种控制混沌的线性间隙反馈方法.该方法由控制相和非控制相组成,通过选取合适的反馈系数和控制相时间,可以获得各种不同的所需稳定的周期轨道.分别对一维的声光双稳系统和二维的类Henon吸引子进行计算机模拟,表明该方法可以使既定的系统按照给定的周期轨道演化,并且是大范围可控的. 关键词： 间隙线性反馈 混沌 类Henon映射 Lyapunov指数     

控制单模激光Haken-Lorenz系统混沌的一种有效方法

基于变量脉冲反馈法(VPF)的设计思想,提出了一种控制非线性系统中混沌的新方法——变量变化率脉冲反馈(VRPF)法.将此方法应用到单模激光Haken-Lorenz系统混沌的控制中,计算机模拟结果表明,通过恰当地选择反馈系数和脉冲间隔,可以将系统稳定在1p、2p、3p…2mp、3np以及2mp×3np这样不同的周期轨道,并且获得同一周期轨道的反馈系数和脉冲间隔并不是唯一的.     

声光双稳态系统混沌的周期扰动控制

声光双稳混沌系统的参量受到进行周期扰动,在一定扰动强度下,可实现对混沌的控制.通过数值模拟,证明该方法的有效性,并计算了系统随扰动强度的状态演化和李雅普诺夫指数演化,揭示了扰动强度与系统状态的关系.在此基础上的实验研究,实验证实了对声光双稳混沌系统进行参量扰动可以有效控制混沌.     

声光双稳系统混沌的控制

对声光双稳系统的混沌态提出参数连续延时反馈的控制技术。数值分析表明，在一定的控制强度下，这种控制使系统在原混沌区具有负的最大李亚普诺夫指数，并且能够保证控制的目标状态是原系统的失稳不动点中稳定周期轨道。文章通过与实验结果的比较，验证了本控制方法的有效性。     

混沌系统的变量变化率反馈控制方法研究

设计了一种控制连续非线性系统中混沌的新方法———变量变化率脉冲反馈 (VRPF)方法 .介绍了VRPF方法的控制原理以及反馈系数和脉冲间隔的选择技巧 .将此方法应用到BZ反应 3D模型系统混沌的控制中 ,计算机仿真模拟显示 ,通过恰当地选择反馈系数和脉冲间隔 ,可以将系统稳定在 1p、2p、3p、4p、…、2 n× 3mp (n、m为整数 )这样不同的周期轨道 ,从而使系统的功率谱也由混沌态时的连续谱转变为具有分立单峰的分立谱 .此外 ,仿真模拟还发现VRPF方法具有极宽的控制域     

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.     

耦合双稳映象格子模型的时空混沌控制

变量反馈技术实现了耦合双稳映象格子模型的时空混沌控制.数值实验结果表明,利用不同的反馈技术和不同的反馈强度,可以将双稳映象系统的混沌及耦合双稳映象格子模型的时空混沌控制到不动点或周期轨道.变量反馈控制法除了局域双稳映象系统的定态点外,不需要先获取耦合双稳映象格子时空系统的动力学信息,它对抑制耦合双稳映象系统中的湍流具有一定的指导作用.     

状态反馈和参数调整控制离散非线性系统的倍周期分岔和混沌

利用系统的状态反馈和参数调节的方法，有效地实现了离散非线性动力系统的倍周期分岔的延迟控制和混沌吸引子中不稳定周期轨道的控制.同时，通过选择合适的调控参数，可以将系统从一个2n周期轨道控制到2m(m关键词： 状态反馈 参量调节 混沌控制 分岔控制     

用周期拍方法控制非线性耗散系统和保守系统的混沌

通过分析无反馈周期拍方法控制耗散系统的动力学特性,找出了控制耗散系统混沌轨道的必要条件,并且对周期拍方法进行推广,在加上作为微扰的反馈项后,实现对2维Hamiltonian系统混沌轨道的控制.对于标准映象,系统的整体混沌轨道被稳定在目标周期轨道上,并且在有较弱外噪声的情况下具有鲁棒性.在3维连续流的情况下,与局限于Poincar e^-截面的脉冲控制方法进行比较,确定了两种控制方法各自的适用范围,结论是,为了稳定控制保守系统的混沌轨道,外加控制项必为耗散的. 关键词： 混沌控制 保守系统     

非线性反馈控制单模激光Haken-Lorenz混沌系统

提出一种变量非线性反馈（VNF）方法控制混沌系统.介绍了该方法的控制原理以及反馈系数的选取原则,以单模激光Haken-Lorenz系统为例对非线性反馈控制方法进行了理论研究.仿真结果显示,通过恰当的选择反馈系数k,使系统的最大李雅普诺夫（Lyapunov）指数由正值转变为负值,相图中系统的轨迹由混沌吸引子转变为周期数为2n×3mp(n、m为整数)的周期轨道.通过与线性反馈控制结果对比发现,非线性反馈控制方法简便有效,控制速度快.     

A new hyperchaotic system and its linear feedback control

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.     

Stability transformation: a tool to solve nonlinear problems

We present an analysis of the properties as well as the diverse applications and extensions of the method of stabilisation transformation. This method was originally invented to detect unstable periodic orbits in chaotic dynamical systems. Its working principle is to change the stability characteristics of the periodic orbits by applying an appropriate global transformation of the dynamical system. The theoretical foundations and the associated algorithms for the numerical implementation of the method are discussed. This includes a geometrical classification of the periodic orbits according to their behaviour when the stabilisation transformations are applied. Several refinements concerning the implementation of the method in order to increase the numerical efficiency allow the detection of complete sets of unstable periodic orbits in a large class of dynamical systems. The selective detection of unstable periodic orbits according to certain stability properties and the extension of the method to time series are discussed. Unstable periodic orbits in continuous-time dynamical systems are detected via introduction of appropriate Poincaré surfaces of section. Applications are given for a number of examples including the classical Hamiltonian systems of the hydrogen and helium atom, respectively, in electromagnetic fields. The universal potential of the method is demonstrated by extensions to several other nonlinear problems that can be traced back to the detection of fixed points. Examples include the integration of nonlinear partial differential equations and the numerical determination of Markov-partitions of one-parametric maps.     

The design and artificial realization of a controller of pulse coupling feedback

In this paper a controller of pulse coupling feedback (PCF) is designed to control chaotic systems. Control principles and the technique to select the feedback coefficients are introduced. This controller is theoretically studied with a three dimensional (3D) chaotic system. The artificial simulation results show that the chaotic system can be stabilized to different periodic orbits by using the PCF method, and the number of the periodic orbits are 2ⁿ× 3^mp (n and m are integers). Therefore, this control method is effective and practical.     

混沌体系中寻找周期轨迹的方法

一个不可积混沌体系，由于扰动而遭到破坏时，存活的周期轨迹体现了体系的本质特征，是 体系的运动骨架.在一定程度上， 可以由周期轨迹来量子化不可积体系，这充分说明了 周期轨迹的重要性.而寻找周期轨迹，也就成为研究混沌体系动力学特性以及对混沌体系进 行量子化的关键问题.结合具体实例，给出了3种常用的寻找周期轨迹方法，并详细探讨了各 种方法的优缺点和适用范围. 关键词： 周期轨迹 数值方法 混沌     

平移法控制离散系统的倍周期分岔和混沌

利用平移系统的方法,实现了对离散非线性动力学系统的倍周期分岔的控制和混沌吸引子不稳定周期轨道的控制.只要选择适当的平移参数,使系统平移到不同位置,就可将系统控制在不同的预期轨道.将此方法应用到Logistic映射和Henon映射中取得了很好的控制效果.     

Heteroclinic Connections Between Periodic Orbits in Planar Restricted Circular Three Body Problem. Part II

We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry. As an application we show that the Planar Restricted Circular Three Body Problem (PCR3BP) corresponding to the Sun-Jupiter-Oterma system possesses an infinite number of symmetric periodic orbits and homoclinic orbits to the Lyapunov orbits. Moreover, we show the existence of symbolic dynamics on six symbols for PCR3BP and the possibility of resonance transitions of the comet. This extends earlier results by Wilczak and Zgliczynski [12]. Electronic Supplementary Material: Supplementary material is available in the online version of this article at An erratum to this article is available at .     

Calculations of periodic orbits: The monodromy method and application to regularized systems

We describe a numerical method for calculating periodic orbits, which is a generalization of the monodromy method by Baranger et al. to the case of an arbitrary autonomous dynamical system. Two variants of the method are developed, using the midpoint and the Runge-Kutta discretization of equations of motion, respectively. Particularly, we adapt the first variant for calculating periodic orbits of Hamiltonian systems when the period or the energy is given a priori. Finally, we consider the application of the monodromy method to the case of regularized mechanical systems and demonstrate the use by two examples. (c) 1999 American Institute of Physics.