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.     

控制信号对控制混沌的作用的实验研究

引入双调谐电路非反馈控制混沌模型.将控制信号加入非线性微分方程的二阶项系数上.实验研究控制信号对控制混沌态的作用:改变控制频率f_k和控制强度I_k,可实现对混沌态的倍周期分频、加周期和准周期控制.研究相位角θ对控制态的作用.观察到呼吸现象并解释其形成的原因.     

混沌记忆系统的自适应反馈控制和轨迹跟踪控制

研究了混沌记忆系统的自适应反馈控制和基于反馈线性化的轨迹跟踪控制问题.首先,通过绘制系统的时域波形图和混沌吸引子图验证系统的复杂的动力学行为;然后,分别应用自适应反馈控制方法和基于反馈线性化的轨迹跟踪控制方法设计控制器,对系统施加控制;最后,通过数值仿真验证控制器的有效性.     

一类Sprott-O混沌系统的H_∞状态控制和自适应控制研究

研究了一类Sprott-O混沌系统的H_∞状态反馈控制和自适应反推控制问题.首先,通过绘制系统的Lyapunov指数图、混沌吸引子图及参数变化时的分岔图等验证了系统在一定参数条件下具有的复杂混沌动力学行为;然后,分别应用H_∞状态反馈控制方法和自适应反推控制方法设计不同的控制器,对混沌系统加以控制;最后,通过数值仿真验证了所设计控制器的有效性.     

分数阶Chen-like系统混沌性态分析及控制

提出了一类Chen-like系统,研究了该系统奇点稳定性、混沌等动力学性态.讨论了Chen-like系中参数与阶数对系统混沌性态的影响,并给出了Chem-like系统出现混沌性态的阶次范围.与分数阶Chen系统相比,系统出现混沌性态的阶次范围增大了.根据分数阶系统稳定性理论及线性反馈控制,对系统进行了混沌控制,得出了混沌系统在平衡点处的稳定性条件.数值模拟验证了理论分析的正确性.     

一类非线性金融系统数学模型的混沌控制

研究一类非线性金融系统数学模型的混沌控制.首先,运用动力学方法研究位移反馈控制、加速反馈控制、增强反馈控制、延迟反馈控制在该系统的应用条件和反馈增益系数.其次,运用数值模拟的方法验证各种控制方法的可行性,比较各种控制方法的应用效果.最后选择较好的控制方法,为金融危机的宏观调控提供建议.     

广义Lorenz系统的全局指数吸引集及其应用

对于一种广义Lorenz系统,通过线性变换和构造广义Lyapunov函数,给出了全局指数吸引集估计的新方法,并给出了最终界的精确估计式.最后,将结果应用到Chen系统和Lü系统的混沌控制中,给出了保持系统指数稳定的一种线性反馈控制,并且反馈控制律具有更少的保守性.     

一个新的四维节能减排系统的动力学分析及其控制

依据一个经济时期内节能减排、碳排放、经济增长和新能源的开发利用之间相互依存、相互制约的演化关系建立了一个新的四维节能减排动态演化模型,这是一类新的非线性微分系统,通过平衡点稳定性、系统的耗散性、Lyapunov指数谱等的分析,研究了系统的基本动力学行为,利用数值模拟的方法给出了系统的动力演化行为;利用线性反馈控制方法将四维节能减排系统的混沌态控制到原先不稳定的平衡点,给出了数值模拟结果,验证了理论分析的正确性.     

一类超混沌离散系统的控制

研究一类超混沌离散系统的控制问题.基于局部线性化建立了时变线性反馈控制律.采用Liapunov直接法估计了控制律可以有效作用的邻域范围.分别给出了应用该控制律解决不稳定周期轨道的镇定问题和任意给定周期轨道的追踪问题的算例.     

一个四翼混沌系统的广义控制与同步

针对四翼混沌系统的控制和同步问题,采用反馈控制方法将系统的混沌运动控制到稳定态;根据Routh-Huriwtz准则获得了系统达到控制目标时反馈系数所满足的条件,通过设计控制器研究系统的广义控制与同步.在此基础上给出了响应系统同时含有控制变量时,系统的广义混合控制与同步运动行为,并从理论分析和Maple数值仿真验证了同步方法的可行性.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in     

ANALYSIS IN THEORY AND APPLICATIONS Vol. 30, 2014 CONTENTS

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An alternative mathematical algorithm for the photo- and videokeratoscope

Due to the resolution of current laser technology, the accuracy of corneal topography as measured by the videokeratoscope is no longer adequate to provide precise enough data for refractive surgery or for the fitting of customized contact lenses. We present an algorithm for recovering corneal topography that makes use of modern differential geometric techniques and numerical descent in Sobolev spaces. We believe this algorithm may be used with the photo- and videokeratoscope to increase the accuracy of the recovered corneal topography.     

A note on Sobolev orthogonality for Laguerre matrix polynomials

Let {Ln(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0, ∞) by Ln(A,λ)(x)=n!/(-λ)n∑nk=0(-λ)κ/k!(n-1)! (A I)n[(A I)k]-1 xk,where A ∈ Cr×r. It is known that {Ln(A,λ)(x)}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) ＞ - 1 for every z ∈σ(A).In this note we show that forA such that σ(A) does not contain negative integers, the Laguerre matrix polynomials Ln(A,λ) (x) are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case.     

CONTENTS OF VOLUME 30

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