一类参数激励非线性振子的周期分岔序列和混沌行为

用数值方法对一类参数激励的非线性DUffing-Van der Pol振子进行了研究.着重考察了系统随周期驱动力角频率ω改变的周期分岔序列及混沌行为.给出了各种振荡态和混沌态随时间的循环模式.发现在一定的ω值区间内,周期运动和混沌运动交替出现,周期运动会失稳直接进入混沌态.对通向混沌的道路问题也作了一些探讨.     

基于MATLAB的各类混沌系统的计算机仿真模拟研究

本文利用数学软件MATLAB对Lorenz混沌系统、Rossler混沌系统进行数值计算和模拟一些混沌现象,同时模拟出各类混沌系统的独特性质,如混沌吸引子、倍周期、初值敏感性、相图、分岔图等。通过观察和分析上述特性,加深了我们对混沌现象的理解。     

含二次非线性项准周期激振系统的混沌

研究了含二次非线性项系统准周期受迫振动和准周期参数激励振动,分析了相应未受援动Hamilton系统的全局结构,应用推广的Melnikov方法建立了混沌存在的必要条件,还考虑了增加激励数目对混沌性态的影响。     

一类广告竞争模型的延迟反馈混沌控制方法

运用延迟反馈混沌控制方法来稳定由企业的广告竞争行为引起的市场混沌更为贴近经济系统的实际，这是因为它体现了竞争主体所采取的控制措施是基于某些市场信号而做出的理性选择。在本文中，我们以一个双寡头垄断广告竞争模型为例，将其控制到各种低周期轨道并成功地实现了系统在混沌态与各种周期轨道间的转换，对市场上企业广告竞争行为的策略选择有重要的启示意义。     

利用脉冲非线性状态反馈控制混沌

研究了脉冲非线性反馈控制方法控制Lorenz系统的混沌问题，首先从理论上论证了控制方法的正确性．然后设计出了三种控制器并给出了控制器应满足的条件，理论分析和数值模拟结果表明混沌Lorenz系统中的不稳定不动点能被稳定控制，而且Hopf分岔也能产生，给出了相应的数值模拟结果，例如不动点、极限环(IP)轨道，采用脉冲控制方法的优点是控制代价小，工程上易于实现，最后指出，对于其他具有平衡点对称的混沌系统如蔡氏电路系统的混沌控制，此控制策略同样有效。     

弱周期微扰法控制双环掺铒光纤激光器混沌

本文提出了一种基于变量与周期信号耦合的弱周期微扰法控制双环掺铒光纤激光器混沌的具体方案。数值模拟结果表明,通过适当调节反馈强度,该方法可实现对双环掺铒光纤激光器混沌和超混沌的控制。     

股市交易群体变动的模型与混沌

金融系统复杂性的研究结果指出，股市交易存在两种类型交易者，即基本交易者和噪声交易者。股市行为基本动因是基本交易者的动态变化所致，而股市波动的另一个原因则是噪声交易者动态行为。本文则研究股市交易群体变动条件下的模型及其混沌问题，分析建立了股市波动模型以至产生混沌的系统条件，并给出金融系统的计算机仿真实验，检验了股市波动产生混沌的条件。     

非线性系统的混沌现象

文章分析了具有混沌动力学特征的非线性三阶自治电路,给出了混沌电路中非线性电阻的构造方法,使用EWB软件对混沌电路进行了计算机仿真,通过实际硬件电路板测试得到混沌吸引子、倍周期分岔、周期性窗口等预期分析结果,此结果对深入研究混沌理论及混沌的同步和控制有积极借鉴作用.     

一类三维混沌系统的自适应同步

针对参数不匹配的两个异结构混沌系统,基于微分方程稳定性理论,给出了一类不同构混沌系统的自适应同步策略.根据两个混沌系统的不同结构、参数互异的特征,选择适当的参数自适应律和自适应控制器,构建同步数学模型,实现了系统的混沌同步.并且通过Matlab软件数值仿真验证了所设控制器的有效性和方法的可操作性。     

一类电力系统分岔的仿真研究

本文为了研究一类经典二维非线性电力系统的分岔现象,介绍了电力系统模型中常见分岔的基本概念,求出系统产生鞍结分岔的条件。利用MATLAB软件对此电力系统的分岔现象进行了数值仿真研究。文中给出了不同参数变化时系统的状态响应曲线。仿真分析验证了鞍结分岔产生的条件,同时直观给出参数变化对电力系统的分岔影响。结论表明,系统的参数变化都会引起系统状态的分岔现象。参数E和参数V随着数值的增大,系统复杂性增加,最后导致混沌,而机械输入功率Pm的变化会引起更复杂的动力学行为,出现周期性的分岔和混沌现象,所以在实际电力系统的运转中要注意对此参数的控制。     

Fuzzy control of dithered chaotic systems via neural-network-based approach

This paper presents an effective approach for controlling chaos. First, a neural-network (NN) model is employed to approximate the chaotic system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of an NN model. Based on the LDI state-space representation, a fuzzy controller is proposed to tame the chaotic system. If the designed fuzzy controller cannot suppress the chaos, a high frequency signal, commonly called dithers, is simultaneously injected into the chaotic system. According to the relaxed method, an appropriate dither is introduced to steer the chaotic motion into a periodic orbit or a steady state. If the frequency of dither is high enough, the trajectory described by the dithered chaotic system and that of its corresponding mathematical model—the relaxed system can be made as close as desired. This phenomenon enables us to get a rigorous prediction of the dithered chaotic system’s behavior by obtaining the behavior of the relaxed system. Finally, a numerical example with simulations is given to illustrate the concepts discussed throughout this paper.     

基于Lyapunov方法Lorenz混沌系统自适应同步方法

对于具有不确定参数的Lorenz混沌系统，通过参数调节和自适应技术讨论了两个同结构Lorenz混沌系统的同步问题。自适应控制器和参数调节律均由Lyapunov稳定行理论来确定。数字仿真表明了该方法的有效性和实用性。     

Design of a model-free adaptive sliding mode control to synchronize chaotic fractional-order systems with input saturation: An application in secure communications

In this work, a model-free adaptive sliding mode control (ASMC) methodology is proposed for synchronization of chaotic fractional-order systems (FOSs) with input saturation. Based on the frequency distributed model and the non-integer version of the Lyapunov stability theorem, a model-free ASMC method is designed to overcome the chaotic behavior of the FOSs. The control inputs are free from the nonlinear-linear dynamical terms of the system because of utilizing the boundedness feature of the states of chaotic FOSs. Moreover, a new medical image encryption scheme is tentatively proposed according to our synchronization method, and its effectiveness is verified by numerical simulations. Furthermore, the performance and security analyses are given to confirm the superiority of the proposed encryption scheme, including statistical analysis, key space analysis, differential attack analysis, and time performance analysis.     

Intermittent control strategy for synchronization of fractional-order neural networks via piecewise Lyapunov function method

In this paper, the synchronization problem of fractional-order neural networks (FNNs) with chaotic dynamics is investigated via the intermittent control strategy. Two types of intermittent control methods, the aperiodic one and the periodic one, are applied to achieve the synchronization of the considered systems. Based on the dynamic characteristics of the intermittent control systems, the piecewise Lyapunov function method is employed to derive the synchronization criteria with less conservatism. The results under the aperiodically intermittent control show more generality than the ones via the periodically intermittent control. For each of the aperiodic and periodic cases, a simple controller design process is presented to show how to design the corresponding intermittent controller. Finally, two numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.     

Design of digital controllers for uncertain chaotic systems using fuzzy logic

A new and systematic method to design digital controllers for uncertain chaotic systems with structured uncertainties is presented in this paper. Takagi-Sugeno (TS) fuzzy model is used to model the chaotic dynamic system, while the uncertainties are decomposed such that the uncertain chaotic system can be rewritten as a set of local linear models with an additional disturbed input. Conventional control techniques are utilized to develop the continuous-time controllers first. Then, the digital controllers are obtained as the digital redesign of the continuous-time controllers using the state-matching approach. The performance of the proposed controller design is illustrated through numerical examples.     

Rank one chaos in a switch-controlled Chua's circuit

In this paper, we study the existence of strange attractors in a switch-controlled Chua's circuit. This circuit is obtained from the original Chua's circuit by adding externally controlled switches to it in such a way to modulate the system state variables. This investigation is conducted from the perspective of a recent chaos theory of rank one maps. The externally controlled switches are used for the purposes of realizing the general settings of the theory. Both synchronous and asynchronous switch control schemes providing periodic kicks in various directions are investigated, and their effects on the resulting chaotic attractors are discussed. The results of the numerical simulations presented are in close agreement with the expectations of the theory.     

Examination of chaotic behaviours using bond graph model

In this paper, modelling and simulation of Chua's chaotic oscillator, which exhibits rich chaotic behaviours, are presented by using the bond graph model. Up to now modelling of Chua's chaotic oscillator using bond graph model is not yet developed. The non-linear resistor in the circuit is modelled in this contribution by linear time-invariant components and ideal switches using piecewise linearization approach. The bond graph model of all the circuit including switches is then generated. Simulations are provided via the computer program called as BOMAS using the obtained bond graph model. Finally, Chua's circuit is verified experimentally. It is shown that all experimental and simulation results well agree with the chaotic behaviours of Chua's circuit.     

混沌的非线性控制

基于逆系统方法设计了控制混沌的非线性控制器，以呈现混沌性态的虫口模型映射和Ｈｅｎｏｎ映射为例给出了控制算例，最后讨论了可能的推广和发展     

Adaptive synchronization of uncertain chaotic systems with adaptive scaling function

The problem of adaptive synchronization for the uncertain chaotic systems with adaptive scaling function is investigated in this paper. In comparison to those of the existing scaling function synchronization, such as the presetting scaling function, the aim of this paper is focused not only on the scaling function but also on the identification of parameters of the chaotic system. Finally, to illustrate the implementation of the proposed method, some numerical simulations are given.