Delta算子框架下混沌系统的自适应滑模控制北大核心CSCD

针对DoS攻击和网络故障下的非线性耦合混沌系统,提出了一种Delta算子框架下自适应滑模控制方法.首先,对连续时间和离散时间的非线性耦合混沌系统,依据Delta算子理论,建立Delta算子框架下的统一模型.其次,对提出的Delta算子框架下的非线性混沌系统设计线性滑模面,并利用线性矩阵不等式方法给出滑模面存在的充分条件.再次,对上述系统提出自适应滑模控制器的设计方法,使之能够快速到达滑模面,实现在DoS攻击和网络故障下的非线性耦合混沌系统的鲁棒镇定.最后,仿真算例结果表明在所设计的自适应滑模控制器下,非线性耦合混沌系统状态稳定,并渐近趋向于零,说明了所提方法的可行性和有效性.     

含间隙非线性弹性超材料的低频宽带机理北大核心CSCD

揭示了基于非线性混沌理论含间隙的非线性局域共振结构的低频宽带形成机理,提出了一类含间隙非线性局域共振结构设计的新理念.在该间隙非线性局域共振系统中,产生了非线性混沌现象,且这种非线性运动可以成功地改变振动噪声中的频谱结构,当系统运动进入混沌状态时,线性谱能量大大削弱,变成了一个连续的宽频谱,进而有效隔离低频线谱.有限元计算结果表明,正是这个间隙引起的非线性混沌现象导致了低频宽带的产生,且理论分析和有限元分析结果高度一致.因此,这类含间隙非线性局域共振弹性超材料结构的设计新思想为局域共振弹性超材料的发展开辟了新天地,且基于非线性混沌理论的低频带隙的形成机理为减振降噪应用研究奠定了非常重要的理论基础.     

分数阶Duffing混沌系统的动力性态及其由单一主动控制的混沌同步

随着物理与技术的深入研究,分数阶非线性系统的动力性态及其分数阶混沌系统的同步成为研究的焦点.研究了分数阶Duffing系统的动力性态包括混沌性质,并且由分数阶非线性稳定性准则得到了分数阶非自治系统的混沌同步.特别地,研究了由单一主动控制的分数阶Duffing系统的同步.相应的数值结果演示了方法的有效性.     

复杂多卷波混沌系统的理论设计与电路实现

双卷波Chua电路的发明第一次在混沌理论与非线性电路之间建立了直接联系.复杂多卷波混沌系统在混沌理论与非线性电路之间架起了桥梁.复杂多卷波混沌系统具有明确的工程应用背景,它的理论设计与电路实现在过去三十年里得到迅猛发展.本文简要的回顾国内外过去三十年在复杂多卷波混沌系统的理论设计与电路实现上的主要研究进展,包括基本理论,设计方法与典型的工程应用,试图推进国内复杂多卷波混沌系统的研究.     

新的分数阶混沌系统及其同步

提出一个新的分数阶混沌系统,该系统含有三个参数,三个非线性项.通过理论分析,给出了分数阶混沌系统存在混沌吸引子的必要条件,通过数值仿真给出了混沌吸引子的图像,接着设计自适应同步控制器和参数自适应律,实现分数阶混沌系统的同步,数值仿真的结果表明设计控制器很好的实现了驱动系统和响应系统的同步.     

一种双寡头垄断Cournot-Puu模型的混沌控制研究

基于非线性动力学的基本原理,研究了经济系统中的双寡头垄断Cournot-Puu模型及其混沌控制方法.Cournot-Puu模型具有双曲线形需求函数和彼此不同的不变边际成本,离散化的差分系统显示出其复杂的非线性、分岔和混沌行为.在此基础上,结合Cournot-Puu模型的基本特征,应用延迟反馈控制方法以及自适应控制方法对该系统的混沌行为进行了研究.在结合实际经济意义的条件下,对该模型的输出进行调整并实现混沌控制.     

非线性弹性梁中的混沌带现象

研究了非线性弹性梁的混沌运动,梁受到轴向载荷的作用。非线性弹性梁的本构方程可用三次多项式表示。计及材料非线性和几何非线性,建立了系统的非线性控制方程。利用非线性Galerkin法,得到微分动力系统。采用Melnikov方法对系统进行分析后发现,当载荷P₀和f满足一定条件时,系统将发生混沌运动,且混沌运动的区域呈现带状。还详尽分析了从次谐分岔到混沌的路径,确定了混沌发生的临界条件。     

Chen混沌系统的非线性全局同步控制

研究了Chen提出的一个新的混沌系统的混沌同步问题,利用非线性控制方法设计了三种混沌同步控制器,并用李雅普诺夫方法证明了在混沌控制器作用下,驱动、响应混沌系统可以实现全局同步.数值仿真结果表明,所设计的三种混沌控制器都能有效的实现混沌同步,并且具有很强的鲁棒性.     

多涡旋混沌同步和分数阶混沌同步

为探讨混沌同步现象和相应的动力学特性,研究了两类特殊的混沌系统即多涡旋混沌系统和分数阶混沌系统的同步.为此,设计了一种非线性反馈控制器,实现了多涡旋类Lorenz的混沌吸引子的投影同步;通过改变投影同步的比例系数,获得了与激励系统相对应的状态变量的任意比例输出.此设计还实现了分数阶超混沌系统的状态向量与任意信号的追踪同步,从而控制分数阶混沌信号趋于期望的周期轨道或平衡点,并实现分数阶混沌系统与整数阶混沌系统的异构追踪同步.最后设计了具有分数阶混沌特性的电路,借助仿真实验证实了分数阶超混沌系统的动力学行为.这些研究结果可以应用于许多领域,例如宏观经济系统的数据分析、保密通讯系统分析与设计等.     

基于Melnikov函数的系统混沌性证明

到目前为止,系统混沌性的证明大多数还局限在数据仿真实验上,理论证明还很少.应用Melnikov函数法讨论了一种非线性系统的同宿轨道和异宿轨道,并给出了系统产生混沌现象所满足的条件.     

Recent development of chaos theory in topological dynamics

We give a summary on the recent development of chaos theory in topological dynamics,focusing on Li–Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.     

币值低估下对外贸易对物价水平的影响

从货币数量方程出发,运用汇率理论与对外贸易理论,主要讨论了币值低估时,对外贸易对经济体内物价水平的影响.在外贸情况一定时,经济体内物价水平与币值低估程度正相关;当币值低估程度确定,进出口比例与外贸规模也会对经济体内的通胀大小产生影响,具体表现为:外贸顺差越大,通胀越严重;但贸易逆差时,仍然有可能出现通胀;而若要追求贸易平衡的目标,则外贸规模越大,通胀越严重.同时,一国的币值低估还通过对外贸易对他国的物价水平产生影响.     

Chaos in a new system with fractional order

The dynamics of fractional-order systems have attracted a great deal of attentions in recent years. With fractional order, the dynamics of a system which includes comprehensive dynamical behaviors, such as fixed point, periodic motion, chaotic motion, and transient chaos is studied numerically in this paper. It is known that chaos exists in the fractional-order system with order less than 3. In this study, the lowest order found for this system to yield chaos is 2.43. The results are validated by the existence of a positive Lyapunov exponent. Period doubling routes to chaos in the fractional-order system are also obtained. Moreover, generation of a four-scroll chaotic attractor by the system is observed.     

扩大再生产条件下的国际价值、 贸易利益与经济增长

以马克思的社会资本再生产理论和国际价值理论为基础,通过阐述社会资本再生产过程中两部门的经济增长与基于国际不等价交换、国际价值与国别价值的比较而形成的国际贸易利益的关系,对国际贸易与经济增长问题进行了简要分析.在国际贸易过程中,基于国际不等价交换的贸易利益或损失会导致各国相关部门的经济增长发生变化,从国际不等价交换中获得较多国际贸易利润的国家及其相关部门,其经济增长率较高;反之,从国际不等价交换中遭受国际贸易利益损害的国家及其相关部门,其经济增长率下降.     

Chaos in fractional-order Genesio-Tesi system and its synchronization

In this paper we study the chaotic dynamics of fractional-order Genesio-Tesi system. Theoretically, a necessary condition for occurrence of chaos is obtained. Numerical investigations on the dynamics of this system have been carried out and properties of the system have been analyzed by means of Lyapunov exponents. It is shown that in case of commensurate system the lowest order of fractional-order Genesio-Tesi system to yield chaos is 2.79. Further, chaos synchronization of fractional-order Genesio-Tesi system is investigated via two different control strategies. Active control and sliding mode control are proposed and the stability of the controllers are studied. Numerical simulations have been carried out to verify the effectiveness of controllers.     

Interpreting supply chain dynamics: A quasi-chaos perspective

Chaotic phenomena, chaos amplification and other interesting nonlinear behaviors have been observed in supply chain systems. Chaos can be defined theoretically if the dynamics under study are produced only by deterministic factors. However, deterministic settings rarely present themselves in reality. In fact, real data are typically unknown. How can the chaos theory and its related methodology be applied in the real world? When the demand is stochastic, the interpretation and distribution of the Lyapunov exponents derived from the effective inventory at different supply chain levels are not similar to those under deterministic demand settings. Are the observed dynamics of the effective inventory random, chaotic, or simply quasi-chaos? In this study, we investigate a situation whereby the chaos analysis is applied to a time series as if its underlying structure, deterministic or stochastic, is unknown. The result shows clear distinction in chaos characterization between the two categories of demand process, deterministic vs. stochastic. It also highlights the complexity of the interplay between stochastic demand processes and nonlinear dynamics. Therefore, caution should be exercised in interpreting system dynamics when applying chaos analysis to a system of unknown underlying structure. By understanding this delicate interplay, decision makers have the better chance to tackle the problem correctly or more effectively at the demand end or the supply end.     

Fractal dimension evolution and spatial replacement dynamics of urban growth

This paper presents a new perspective of looking at the relation between fractals and chaos by means of cities. Especially, a principle of space filling and spatial replacement is proposed to interpret the fractal dimension of urban form. The fractal dimension evolution of urban growth can be empirically modeled with Boltzmann’s equation. For the normalized data, Boltzmann’s equation is just equivalent to the logistic function. The logistic equation can be transformed into the well-known 1-dimensional logistic map, which is based on a 2-dimensional map suggesting spatial replacement dynamics of city development. The 2-dimensional recurrence relations can be employed to generate the nonlinear dynamical behaviors such as bifurcation and chaos. A discovery is thus made in this article that, for the fractal dimension growth following the logistic curve, the normalized dimension value is the ratio of space filling. If the rate of spatial replacement (urban growth) is too high, the periodic oscillations and chaos will arise. The spatial replacement dynamics can be extended to general replacement dynamics, and bifurcation and chaos mirror a process of complex replacement.     

Chaos and Shadowing Around a Heteroclinically Tubular Cycle With an Application to Sine-Gordon Equation

The theory of chaos and shadowing developed recently by the author is amplified to the case of a heteroclinically tubular cycle. Specifically, let F be a   C ³  diffeomorphism on a Banach space. F has a heteroclinically tubular cycle that connects two normally hyperbolic invariant manifolds. Around the heteroclinically tubular cycle, a Bernoulli shift dynamics of submanifolds is established through a shadowing lemma. As an example, a sine-Gordon equation with a chaotic forcing is studied. Existence of a heteroclinically tubular cycle is proved. Also proved are chaos associated with the heteroclinically tubular cycle, and chaos cascade referring to the embeddings of smaller-scale chaos in larger-scale chaos.     

上海市国际服务贸易收入和支出的统计分析

本文通过因子分析将指标进行分类,对2000-2007年上海市国际服务贸易收入和支出的数据进行统计分析。同时,通过回归分析从理论上提出对国际服务贸易收入和支出的预报和控制方法。最后对文章中提到的模型进行使用说明,并提出对上海市国际服务贸易发展的一些建议。     

以混沌理论为基础的神经网络预测方法

我国证券市场股价波动表现出特有的混沌性质，具有局部随机与整体秩序相容的特征。本以2002年每隔十秒的上证指数高频数据为例，以混沌理论为基础。从原始序列中构造出若干个新的时间序列，运用神经网络法进行预测。预测结果表明，此方法能够较好地预测股票的走势，有望在股票交易中应用。