强迫布鲁塞尔振子中的阵发混沌

用数值计算证实了在周期外力作用下的三分子反应模型(布鲁塞尔振子)中存在着走向混沌状态的阵发道路。研究了阵发混沌的发展过程。讨论了数值研究中区分阵发混沌和暂态过程的方法。我们的工作进一步说明,原来在参数空间中发现的嵌在混乱带中的大片周期为3的区域(以及周期为4,5,6,7等的较小区域),对应于一维非线性映象相像的切分岔)每个切分岔开始前均可看到阵发混沌。因此,走向混沌的倍周期分岔道路和阵发道路乃是孪生现象,应在更多的由非线性微分方程描述的系统中观察到。 关键词：     

强迫布鲁塞尔振子中从准周期运动到混沌态的过渡

我们在周期外力作用下的布鲁塞尔振子中发现了从准周期行为到混沌态的过渡。这样,强迫布鲁塞尔振子成为数值实验中第一个同时看到各种通向混沌的道路并存的模型,而这是与某些流体力学实验一致的。原来光滑的周期采样图在局部起皱折迭,同时准周期的功率谱中出现越来越多的噪声背景,这种过渡方式与人们在圆周映象中讨论的准周期轨道全局失去光滑性成为对比,可能在非线性微分方程所描述的系统中更具有代表性。 关键词：     

随机参数Duffing系统中的随机混沌及其延迟反馈控制

研究了谐和激励下含有界随机参数Duffing系统(简称随机Duffing系统)中的随机混沌及其延迟反馈控制问题.借助Gegenbauer多项式逼近理论，将随机Duffing系统转化为与其等效的确定性非线性系统.这样，随机Duffing系统在谐和激励下的混沌响应及其控制问题就可借等效的确定性非线性系统来研究.分析阐明了随机混沌的主要特点，并采用Wolf算法计算等效确定性非线性系统的最大Lyapunov指数，以判别随机Duffing系统的动力学行为.数值计算表明，恰当选取不同的反馈强度和延迟时间，可分别达到抑制或诱发系统混沌的目的，说明延迟反馈技术对随机混沌控制也是十分有效的. 关键词： 随机Duffing系统 延迟反馈控制 随机混沌 Gegenbauer多项式     

基于线性矩阵不等式的一类新羽翼倍增混沌分析与控制

在对已有的混沌系统分析和研究的基础上,将一个二次混沌系统第三个方程关于x的线性项引入到第二个方程中,通过对该系统第二个等式中的线性项x作绝对值运算,提出了一类新的二次非线性系统.采用非线性动力学方法分析了系统参数变化时所经历的稳定、准周期、混沌的过渡过程,模拟电路实验结果与Matlab数值仿真结果相一致.分析发现混沌态时绝对值运算后的系统比原系统的Lyapunov指数更大,并可将原系统的混沌吸引子由两个翼的拓扑结构变为四翼的拓扑结构,从而实现羽翼倍增.针对该混沌特性更强的羽翼倍增混沌系统,基于Takagi-Sugeno(T-S)模糊模型和线性矩阵不等式(LMI),设计出使该羽翼倍增混沌系统渐近稳定的鲁棒模糊控制器.仿真结果证实了所提出定理和设计控制器的有效性.     

基于忆阻器的时滞混沌系统及伪随机序列发生器

忆阻器作为可调控的非线性元件,很容易实现混沌信号的产生.基于忆阻器的混沌系统是当下研究的热点,但是基于忆阻器的时滞混沌系统目前却鲜有人涉足.因此,本文提出了一个新型忆阻时滞混沌系统.时延的存在增加了系统的复杂性,使系统能够产生更丰富、更复杂的动力学行为.我们对提出的忆阻时滞混沌系统进行了稳定性分析,确定了显示系统稳定平衡点的相应参数区域.讨论了在不同参数情况下的系统状态,系统呈现出形态各异的混沌吸引子相图,表现出丰富的混沌特性和非线性特性.最后,将系统用于产生伪随机序列,并经过实验验证,我们提出的系统具有良好的自相关性和互相关性,同时能获得相对显著的近似熵.该时滞混沌系统具有复杂的动力学行为和良好的随机性,能满足扩频通信和图像加密等众多领域的应用需要.     

含一个非线性项混沌系统的线性控制及反控制

研究了一类仅含一个非线性项混沌系统的线性控制与反控制,根据Routh-Hurwitz稳定性条件,先对这类混沌系统进行控制,使其达到稳定的状态,然后改变控制系数,使其再次产生混沌,得到一个新的混沌系统,并对这个新的混沌系统的基本动力学行为进行了分析,数值仿真也验证了新系统的混沌性态.     

非线性光电延时反馈混沌同步复用通信系统研究

提出了一种基于电光调制器的非线性光电延时反馈超混沌复用通信系统.与传统混沌通信系统不同,其混沌波形不是由激光器产生,而是由电光调制器产生,该系统具有非线性维数高、易于再生和精确控制的优势.介绍了信号调制反馈延时的编码方法和相关检测解码方法,数值仿真了三条支路的高速复用与解复用,分析了误码产生的主要原因,并进一步研究了光...     

单模激光混沌特性的理论研究

在光学中，激光是产生双稳态、振荡、混沌等多种自组织现象的典型例子。本文采用非线性理论分析了单模激光的混沌特性，对描述单模激光的非线性动力学方程进行了稳定性分析，从而确定了系统失稳后进入混沌态的分歧点，并利用计算机进行了数值计算，给出了系统呈现混沌态的模拟结果。计算机数值模拟的结果与理论分析的结果相吻合。     

网络交通流动态演化的混沌现象及其控制

本文以含2条平行路径的交通网络为例, 探讨了网络交通流逐日动态演化问题. 首先, 建立了动态系统模型来刻画网络交通流的演化过程, 动态系统模型的不动点就是随机用户平衡解, 证明了平衡解存在且唯一. 然后, 根据非线性动力学理论, 推导出了网络交通流演化的稳定性条件. 其次, 通过数值实验, 分析了网络交通流的演化特征, 发现了在一定条件下流量的周期振荡和混沌现象. 最后, 以OD需求为控制变量推导出了网络交通流混沌控制的方法.     

离子迁移忆阻混沌电路及其在语音保密通信中的应用

忆阻器是一种具有记忆功能和纳米级尺寸的非线性元件, 作为混沌系统的非线性部分, 能够使系统的物理尺寸大大减小, 同时可以得到各种丰富的非线性曲线, 提高混沌系统的复杂度和信号的随机性. 因此, 本文采用离子迁移忆阻器的磁控模型设计了一个新的混沌系统. 通过理论推导、数值仿真、Lyapunov指数谱、分岔图和Poincaré截面图研究了系统的基本动力学特性, 并分析了改变不同参数时系统动力学行为的变化. 同时, 建立了模拟该系统的SPICE电路, SPICE仿真结果与数值分析相符, 从而验证该混沌系统的混沌产生能力. 最后, 利用线性反馈同步控制方法实现了新构造的离子迁移忆阻混沌系统的同步, 并且采用该同步方法有效实现了语音信号的保密通信. 数值仿真证实了新混沌系统的存在性以及同步控制应用的可行性.     

A strange attractor of the Smale-Williams type in the chaotic dynamics of a physical system

A nonautonomous nonlinear system is constructed and implemented as an experimental device. As represented by a 4D stroboscopic Poincaré map, the system exhibits a Smale-Williams-type strange attractor. The system consists of two coupled van der Pol oscillators whose frequencies differ by a factor of two. The corresponding Hopf bifurcation parameters slowly vary as periodic functions of time in antiphase with one another; i.e., excitation is alternately transferred between the oscillators. The mechanisms underlying the system’s chaotic dynamics and onset of chaos are qualitatively explained. A governing system of differential equations is formulated. The existence of a chaotic attractor is confirmed by numerical results. Hyperbolicity is verified numerically by performing a statistical analysis of the distribution of the angle between the stable and unstable subspaces of manifolds of the chaotic invariant set. Experimental results are in qualitative agreement with numerical predictions.     

Application of a model of nonlinear history-dependent magnetic behavior for inductance estimation of a microinductor

This paper presents a method for the numerical inductance calculation of a passive electromagnetic inductive device using cores made of a nonlinear magnetic material. The material model used for this purpose describes the nonlinear magnetic behavior by a set of differential equations. The coupled implicit system of Maxwell equations and material model equations is solved by a simplified algorithm which shall be explained while applied to a new design of a microinductor, the so called I-inductor.     

Model equations from a chaotic time series

We present a method for obtaining a set of dynamical equations for a system that exhibits a chaotic time series. The time series data is first embedded in an appropriate phase space by using the improved time delay technique of Broomhead and King (1986). Next, assuming that the flow in this space is governed by a set of coupled first order nonlinear ordinary differential equations, a least squares fitting method is employed to derive values for the various unknown coefficients. The ability of the resulting model equations to reproduce global properties like the geometry of the attractor and Lyapunov exponents is demonstrated by treating the numerical solution of a single variable of the Lorenz and Rossler systems in the chaotic regime as the test time series. The equations are found to provide good short term prediction (a few cycle times) but display large errors over large prediction time. The source of this shortcoming and some possible improvements are discussed.     

Optically injected laser system: characterization of chaos, bifurcation, and control

A single mode semiconductor laser subjected to optical injection, described by a set of three coupled nonlinear ordinary differential equations, exhibiting chaos is considered. By means of a recurrence analysis, quantification of the strange attractor is made. Analytical studies of the system using asymptotic averaging technique, derive certain conditions describing the prediction of 1-->2 bifurcation, which have subsequently been verified on numerical simulation. Furthermore, the locus of points on the parameter phase space representing Hopf bifurcation has been derived. The problem of control of chaos by a new procedure based on adaptive stabilization is also addressed. The results of such control are shown explicitly. Though this analysis deals with a very specific set of equations, the overall features that come out of the study remains valid for almost all laser systems.     

Nonlinear parametric effects and dynamic chaos in a nonautonomous oscillating system with a nonlinear capacitance

A mathematical model is constructed of a nonautonomous dynamic system containing a nonlinear capacitance and possessing a four-dimensional phase space. A numerical investigation is performed of branching processes and phenomena accompanying variations in the frequency and amplitude of an external force. The existence of complex dynamic processes that are a combination of a nonlinear force resonance and a parametric resonance is demonstrated. It is found that both a strange chaotic and a strange nonchaotic attractor exist in the phase space. It is shown that, in the case of a single-frequency external force, the latter attractor exhibits the property of roughness. The results of numerical calculations are confirmed by the results of laboratory experiments.     

Intermittency at the onset of stochasticity in nonlinear resonant coupling processes

A simple model for the nonlinear saturation of a plasma instability is studied via numerical solution of the resonant three-wave coupling equations. When parameters are varied the attractors of motion undergo bifurcations of several types. Intermittency is shown to occur in a transition from a limit cycle to a strange attractor. Such a transition might be indicative of an intermittent onset of turbulence in certain plasma experiments.     

非线性系统混沌运动的神经网络控制

设计前馈反传神经网络控制非线性系统混沌运动的新方法.根据扰动参数模型输入输出数据,按照非线性学习算法训练网络产生系统稳定所需的小扰动控制信号,去镇定混沌运动,使嵌入在混沌吸引子中的不稳定周期轨道回到稳定不动点上.Hnon映射数值仿真结果表明,这种方法控制非线性混沌系统响应速度快、控制精度高 关键词： 混沌控制 神经网络 吸引子 非线性     

光电延迟反馈系统几种混沌路径的仿真分析

对非线性光电延迟反馈系统的响应时间序列进行数值分析.模型反馈循环中加入带通滤波器,建立非线性光电延迟反馈系统的数学模型.用龙格-库塔数值分析方法,通过调节参数,发现两种产生混沌信号的路径.设置特定φ时,在低反馈增益情况下,系统输出快速方波信号或慢速周期震荡信号,随着反馈增益的增加,系统输出出现复杂周期信号或混沌breather现象;在高反馈增益时,系统输出从不同的动力特性变成混沌状态.