雷达角闪烁的混沌特性研究

在雷达目标跟踪和控制系统中,雷达角闪烁的大小与目标丢失和误判的概率紧密相连。采用相位梯度法从理论上对共线多散射中心目标的双散射中心和五散射中心的角闪烁进行仿真建模得到了两组角闪烁仿真序列,按照图形电磁学(GRECO)算法对一种典型目标的螺旋运动角闪烁进行了计算,并参考国外学者非线性动力学研究成果设计了一种综合和有效的混沌判定算法计算流程,用洛伦兹吸引子对此算法进行了验证,最后,对各角闪烁时间序列进行混沌仿真验证。混沌验证算法流程首先计算最佳时间延迟和最小嵌入维数,重构吸引子,得到吸引子、庞加莱截面和主分量谱图三种定性判据与关联维数和最大Lyapunov指数两种定量判据的判定结果,依据混沌判定准则及对比洛伦兹吸引子的验证结果,验证了角闪烁的混沌特性,为抑制角闪烁和降低丢失目标概率拓展了新思路。     

一类离散Hopfield网络的吸引特性研究

该文以n维超立方体为大规模局域连接模型的离散Hopfield网络(简称An网)为研究对象,深入讨论了这种网络的吸引特性,包括吸引子/吸引环的结构和吸引半径等,得出了具有相同结构的吸引子/吸引环具有相同的吸引特性和吸引半径,并给出了它们的吸引半径;进一步地,本文将上述讨论扩展到较为一般的离散Hopfield网络,讨论了它们的吸引子/吸引环与An网的吸引子/吸引环相同(或部分相同)的条件,以及相应的吸引子/吸引环的吸引半径,得出了迁移越大,保留An网吸引子/吸引环的数目越少,且吸引半径越小的结论。     

一种具有多对称同质吸引子的四维混沌系统的超级多稳定性研究

该文在一个经典3维混沌系统的基础上提出一个新的具有超级多稳定性的4维混沌系统。新系统具有一个线平衡点,可以产生无限多对称的同质吸引子。通过相轨图和庞加莱截面等方法分析了系统的混沌特性。重点利用相轨图、分岔图和Lyapunov指数谱等方法分析了初始条件对系统超级多稳定性的影响,分析表明该系统具有很大的初值变化范围,除零点外恒定的Lyapunov指数谱,中心对称的离散分岔图。进一步地,该文研究了系统初值对称性与吸引子对称性的关系,不同于现有混沌系统中的对称吸引子,该系统可以产生无限多对称的同质吸引子。最后,利用电路仿真软件搭建模拟电路捕捉该系统的混沌吸引子,其结果验证了数值仿真的正确性。     

N-涡卷超混沌吸引子产生与同步的研究

四阶MCK电路的主要特点是产生双涡卷超混沌吸引子.本文提出在该电路中产生N-涡卷超混沌吸引子的一种新方法.构造一个具有2N-1个分段线性的奇函数,其构造方法是使该函数中的每一个平衡点分别位于相邻两个转折点的正中间,并保持混沌吸引子中涡卷与键带的相互间置,在此基础上利用递推的方法求得该函数中的各个递推参数,从而可在MCK电路中产生N-涡卷超混沌吸引子.基于李雅普诺夫稳定性理论,研究了两个N-涡卷超混沌吸引子的单向耦合同步问题.最后给出了N-涡卷超混沌吸引子产生及其同步的计算机数值模拟结果.     

取样鉴相数字合成器环中的混沌动力学行为

分析和研究取样鉴相数字合成器环中的混沌动力学行为,根据Ushio与Hira等人的方法,从理论上证明了当系统参数满足一定条件时,系统会出现分岔现象,并具体计算出系统在各个不动点处的Hopf分岔集、系统的李雅普诺夫指数以及豪斯道夫维数。通过对系统进行计算机模拟,观察到系统的奇异吸引子,奇异吸引子的自相似性,系统在混沌状态下对初始条件的灵敏依赖性,进一步证实了三角形取样鉴相数字合成器环中存在混沌现象。     

独立分量分析在混沌信号分析中的应用

本文从高阶统计信息角度来研究混沌信号,利用独立分量分析(Independent Component Analysis以下简称ICA)来探求混沌信号的特征结构.集中讨论了两个问题.一是基于ICA及相关的近似熵提出了一种新的方法来解决相空间重构中最佳延迟的选择问题;二是利用ICA来实现局部本征维数(LID)求取算法,从而对混沌吸引子的维数进行估计.实验结果表明该方法能正确分别混沌信号与非混沌信号,尤其是能正确判别1/f随机过程不是混沌过程.     

三维混沌信号产生器的设计

混沌电路的设计是混沌通信和混沌加密等应用的先决条件,因此混沌电路的理论研究和设计具有十分重要的意义.本文对作者以前提出的二维混沌电路的方法进行推广,论述如何在三维空间中构造混沌吸引子,从而产生混沌信号.该方法的最大优点是:采用模块化设计思路,混沌吸引子的形状可以根据实际需要来设计,易于电路和集成电路实现.     

基于重建相空间的衰落信道非线性预测算法

基于多径快速衰落信道所具有的混沌行为,利用坐标延迟,重建系统的相空间和混沌吸引子,从而获得比标量时间序列更多的系统信息,另外从非线性动力学的角度讨论了快速衰落信道的可预测性,并根据混沌吸引子的稳定性和分形性,提出了非线性快速衰落信道的预测算法,通过引入加权函数,平衡了预测点的邻域对于预测所提供的信息.最后对65.9毫秒的数据进行了预测,仿真结果表明该算法适于进行较大时间范围的预测,预测性能高于无加权预测算法,在信噪比大于15dB时,预测结果可以接受.     

新型多翼统一混沌系统

通过引入多个线性状态反馈控制项和非线性状态反馈控制项,提出了一个新型多翼统一混沌系统。在不同的系统参数下均能产生关于原点对称的真实四翼混沌吸引子,还能产生蝴蝶吸引子、蝙蝠形吸引子和新型多翼混沌吸引子。采用常规的动力学分析方法研究了产生新型多翼混沌吸引子系统的基本动力学特性,例如相图、耗散性分析、李雅普诺夫指数谱和分岔图。结果表明系统可以产生丰富的混沌行为,该新型多翼混沌吸引子可以随参数的变化实现关于x轴对称的双翼混沌吸引子和关于原点对称的真实四翼混沌吸引子。     

含两个磁控忆阻器的五阶混沌电路设计

基于经典蔡氏混沌振荡电路,利用2个磁控光滑忆阻器以及电容、电感设计了一种新的五阶混沌振荡电路。讨论了平衡点稳定性,分析了相图、Lyapunov指数和分岔图。此双忆阻混沌电路具有复杂的动力学行为,运动轨迹依赖于电路参数和电路初始状态;从能量的角度探索了奇异吸引子,结果表明系统存在不同吸引子共存的多稳态现象。用PSpice进行了电路设计,验证了Matlab理论仿真正确性和电路设计的可实现性。     

类Henon吸引子相空间演化行为研究

本文是对类Ｈｅｎｏｎ吸引子的完善，讨论了频率因子对其相空间演化的影响，在一定的频率范围内，该吸引子的混沌特性能够保持，且具有明显的分形特性，但此频带非常窄，频带外吸引子或空间发散，或对精度要求苛刻，从而无法实现稳定的混沌，然后讨论了频率和位相对类Ｈｅｎｏｎ吸引子的共同影响，对各为在相关吸引子的演化特性做了对比和总结。     

忆阻开关混沌电路及其吸引子共存现象研究

为了研究忆阻开关电路的动力学行为,该文提出一种具有多吸引子共存现象的忆阻开关混沌电路。在该电路中存在多吸引子分岔,当系统中发生边界碰撞之后,系统中将产生不同的吸引子共存现象。其中包括单周期极限环与混沌吸引子共存,不同的混沌吸引子共存,对称的2周期极限环共存现象,以及对称的2周期极限环与5周期极限环共存现象等。该文通过相图、分岔图等数值仿真,分析了该电路的动力学行为,并利用PSIM电路仿真验证了其电路的可行性,对开关电路中多吸引子共存现象和混沌应用的研究具有重要意义。     

The multi-scroll hyper-chaotic coexistence attractors and its application

Applying a chaotic system to digital image communication is an effective way to resist the attack of intelligent system with strong computing power. However, the traditional chaotic systems lack more complex dynamic behavior that is very valuable for a series of applications. Based on Lorenz system, this study proposes a hyper-chaotic system with multi-scroll coexistence attractors by using a piecework function. Through bifurcation diagram and Lyapunov exponents, we analyzed the dynamic behavior of the system, and observed multi-scroll coexistence attractors in the numerical simulation. The results show that compared with the traditional chaotic attractor, multi-scroll coexistence attractor has more complex structure and dynamic behavior. Furthermore, we design a cryptosystem based on this system for the digital image. Scrambling and diffusing images with the sequence of multi-scroll coexistence attractors can destroy the correlation of adjacent pixels and hide the information of all pixels. Theoretical analysis and simulation on key space, histogram, information entropy, key sensitivity and pixel correlation show that the encryption scheme is feasible and secure.     

Feature Extraction Based on Speech Attractors in the Reconstructed Phase Space for Automatic Speech Recognition Systems

In this paper, a feature extraction (FE) method is proposed that is comparable to the traditional FE methods used in automatic speech recognition systems. Unlike the conventional spectral‐based FE methods, the proposed method evaluates the similarities between an embedded speech signal and a set of predefined speech attractor models in the reconstructed phase space (RPS) domain. In the first step, a set of Gaussian mixture models is trained to represent the speech attractors in the RPS. Next, for a new input speech frame, a posterior‐probability‐based feature vector is evaluated, which represents the similarity between the embedded frame and the learned speech attractors. We conduct experiments for a speech recognition task utilizing a toolkit based on hidden Markov models, over FARSDAT, a well‐known Persian speech corpus. Through the proposed FE method, we gain 3.11% absolute phoneme error rate improvement in comparison to the baseline system, which exploits the mel‐frequency cepstral coefficient FE method.     

Characteristics of transients among periodic attractors controlledby high-frequency injection in a chaotic laser diode

We numerically studied statistics of the transient response time when switching between periodic attractors obtained through chaos control with a high-frequency injection method in a laser diode that is subject to optical feedback. Each transient response time significantly depends on its position in the starting attractor, whereas the statistical distributions of the response times for many transients are determined almost entirely by the final attractor. The average transient response time is 40 times larger than the round time in the controlled periodic attractors. The transient response time is also strongly affected by the external cavity length. The shortest average transient response time is obtained at a minimum external cavity length and a zero phase difference between the laser field and the feedback light field     

A two-directional grid multiscroll hidden attractor based on piecewise linear system and its application in pseudo-random bit generator

In this work, we present a methodology to design dynamical systems that display two-directional grid multiscroll hidden attractors. Self-excited attractors based on piecewise linear systems emerging from its equilibria in order to exhibit in one-directional (1D) and two-directional (2D) grid multiscroll hidden attractors. The particularity of this methodology is that the self-excited multiscroll attractor is separated into several double scroll self-excited attractors to allow the appearance of a hidden attractor. Next, the hidden attractor is used as the core of a cryptographic safe pseudo-random bit generator and statistical evidence is provided to ensure its convenience in cryptographic applications.     

Design and implementation of n-scroll chaotic attractors from a general jerk circuit

This paper proposes a novel nonlinear modulating function approach for generating n-scroll chaotic attractors based on a general jerk circuit. The systematic nonlinear modulating function methodology developed here can arbitrarily design the swings, widths, slopes, breakpoints, equilibrium points, shapes, and even the general phase portraits of the n-scroll chaotic attractors by using the adjustable sawtooth wave, triangular wave, and transconductor wave functions. The dynamic mechanism and chaos generation condition of the general jerk circuit are further investigated by analyzing the system stability. A simple block circuit diagram, including integrator, sawtooth wave and triangular wave generators, buffer, switch linkages, and voltage-current conversion resistors, is designed for the hardware implementations of various 3-12-scroll chaotic attractors via switchings of the switch linkages. This is the first time to experimentally verify a 12-scroll chaotic attractor generated by an analog circuit. In particular, the recursive formulas of system parameters and real physical circuit parameters are rigorously derived for the hardware implementations of the n-scroll chaotic attractors. Moreover, the adjustability of the nonlinear modulating function and the rigorous recursive formulas together provide a theoretical principle for the hardware implementations of various chaotic attractors with a large number of scrolls.