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lorenz系统的可预报性

物理学报 2006年第2期55卷 969-977页

作者：何文平封国林董文杰李建平扬州大学物理科学与技术学院扬州225002 国家气候中心中国气象局气候研究开放实验室北京100081 中国科学院大气物理研究所东亚区域气候-环境重点实验室北京100029

定义一个动态窗口,以lorenz模型为预报方程,通过对落入动态窗口中的粒子数和平均预报X分量随积分时间演化规律的分析,从另一个角度初步研究了lorenz系统的可预报性问题,并讨论了高斯白噪声对系统可预报性的影响.结果表明,落入动态窗口... 详细信息

定义一个动态窗口,以lorenz模型为预报方程,通过对落入动态窗口中的粒子数和平均预报X分量随积分时间演化规律的分析,从另一个角度初步研究了lorenz系统的可预报性问题,并讨论了高斯白噪声对系统可预报性的影响.结果表明,落入动态窗口中的粒子数在一定程度上反映了系统的可预报性,处于不同区域的初值集合预报时限各不相同,且不同区域内的初值对于小扰动的敏感程度不一样;对于不同区域内的初值集合,高斯白噪声对系统的可预报时限的影响各不相同.

关键词：可预报性 lorenz 动态窗口

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混沌lorenz系统延迟反馈控制的机理分析

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控制理论与应用 2004年第2期21卷 205-210页

作者：闵富红王执铨南京理工大学自动化系江苏南京210094 南京师范大学电气与电子工程学院江苏南京210042

利用广义Hamilton系统理论的Melnikov方法,严格分析了延迟反馈方法控制混沌lorenz系统到周期解的机理,揭示了延迟时间与控制混沌的关系.延迟反馈项实际上是一个作用明显的扰动项,通过选择合适的参数,使得系统的稳定流形与不稳定流形不... 详细信息

利用广义Hamilton系统理论的Melnikov方法,严格分析了延迟反馈方法控制混沌lorenz系统到周期解的机理,揭示了延迟时间与控制混沌的关系.延迟反馈项实际上是一个作用明显的扰动项,通过选择合适的参数,使得系统的稳定流形与不稳定流形不再横截相交,Smale意义下的混沌受到抑制,将lorenz混沌系统引导到各种不同的周期轨道;可见,延迟时间关系到控制扰动量的大小,但不必是混沌吸引子内嵌不稳定周期轨道的周期整数倍.另外,通过数值仿真,其结果与理论分析相符,从而表明了该分析方法的有效性.

关键词：混沌广义Hamilton系统理论 Melnikov方法 lorenz 延迟时间

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Chaos Synchronization of Uncertain lorenz System via Single State Variable Feedback

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Applied Mathematics 2013年第11期4卷 7-12页

作者： Fengxiang Chen Tong Zhang School of Automotive Studies Tongji University Shanghai China Clean Energy Automotive Engineering Center Tongji University Shanghai China

This paper treats the problem of chaos synchronization for uncertain lorenz system via single state variable information of the master system. By the Lyapunov stability theory and adaptive technique, the derived controller is featured as follows: 1) only single state variable information of the master system is needed;2) chaos synchronization can also be achieved even if the perturbation is occurred in some parameters of the master chaotic system. Finally, the effectiveness of the proposed controllers is also illustrated by the simulations as well as rigorous mathematical proofs.

关键词： Uncertain lorenz System Single State Variable Chaos Synchronization

A New Chaotic Behavior from lorenz and Rossler Systems and Its Electronic Circuit Implementation

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Circuits and Systems 2011年第2期2卷 101-105页

作者： Qais H. Alsafasfeh Mohammad S. Al-Arni 不详

This paper presents a new three-dimensional continuous autonomous chaotic system with ten terms and three quadratic nonlinearities. The new system contains five variational parameters and exhibits lorenz and Rossler like attractors in numerical simulations. The basic dynamical properties of the new system are analyzed by means of equilibrium points, eigenvalue structures. Some of the basic dynamic behavior of the system is explored further investigation in the Lyapunov Exponent. The new system examined in Matlab-Simulink and Orcad-PSpice. An electronic circuit realization of the proposed system is presented using analog electronic elements such as capacitors, resistors, operational amplifiers and multipliers.

关键词： Chaos lorenz System Rossler System Lyapunov Exponent Bifurcation

Adaptive Lag Synchronization of lorenz Chaotic System with Uncertain Parameters

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Applied Mathematics 2012年第6期3卷 549-553页

作者： Yanfei Chen Zhen Jia Guangming Deng College of Science Guilin University of Technology Guilin China

The paper discusses lag synchronization of lorenz chaotic system with three uncertain parameters. Based on adaptive technique, the lag synchronization of lorenz chaotic system is achieved by designing a novel nonlinear controller. Furthermore, the parameters identification is realized simultaneously. A sufficient condition is given and proved theoreticcally by Lyapunov stability theory and LaSalle’s invariance principle. Finally, the numerical simulations are provided to show the effectiveness and feasibility of the proposed method.

关键词： Lag Synchronization Adaptive Technique Uncertain Parameters lorenz Chaotic System

Impulsive Control for Synchronization of lorenz Chaotic System

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Journal of Software Engineering and Applications 2012年第12期5卷 23-25页

作者： Wenxiang Zhang Zhanji Gui Kaihua Wang School of Mathematics and Statistics Hainan Normal University Haikou Hainan China

Chaotic synchronization is the key technology of secure communication. In this paper, ?an impulsive control method for chaotic synchronization of two coupled lorenz chaotic system was proposed. The global asymptotic synchronization of two lorenz systems was realized by using the linear error feedback of the state variables of the drive system and the response system as impulsive control signal. Based on stability theory of impulsive differential equation, conditions were obtained to guarantee the global asymptotic synchronization of two lorenz systems. The theory analysis and computer simulation results validated its effectiveness.

关键词： lorenz system Impulsive control Synchronization

PCIM, A Bridge Connecting China and World Power Electronics Industry-Interview with Mr. Udo Weller, president of Mesago PCEM and Dr. lorenz, General Chair of PCIM China

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变频器世界 2006年第4期 35-39页

作者： Mr.Udo Weller Dr.lorenz of Mesago PCIM Chair of PCIM China

PCIM China, international conference and exhibition for power electronics, was held in Shanghai on March 21, 2006. PCIM is one of the most authoritative organizations and has won good reputation overseas for a long ti... 详细信息

关键词： PCIM president of Mesago PCEM and Dr A Bridge Connecting China and World Power Electronics Industry-Interview with Mr General Chair of PCIM China lorenz Udo Weller World

Hopf Bifurcation Control in a lorenz Type System

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Journal of Applied Mathematics and Physics 2018年第8期6卷 1704-1719页

作者： P. E. Calderon-Saavedra E. Munoz-Aguirre J. Alvarez-Mena S. Gomez-Perez Universidad del Tolima Ibagué Colombia Universidad Veracruzana Veracruz Mexico

In this paper Hopf bifurcation control is implemented in order to change the bifurcation from supercritical to subcritical in a differential equations system of lorenz type. To achieve this purpose: first, a region of parameters is identified where the system has a supercritical Hopf bifurcation;second, a class of non-linear feedback control laws is proposed;finally, it is shown that there are control laws which the disturbed system undergoes subcritical Hopf bifurcation.

关键词： lorenz Type Systems Bifurcation Control Hopf Bifurcation Control Subcritical and Supercritical Hopf Bifurcation

Effects of second diffusing component and cross diffusion on primary and secondary thermoconvective instabilities in couple stress liquids

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Applied Mathematics and Mechanics(English Edition) 2017年第11期38卷 1579-1600页

作者： R.RAVI C.KANCHANA P.G.SIDDHESHWAR Department of Humanities and Sciences National Institute of Technology GoaGoa 403401India Department of Mathematics Jnana Bharathi CampusBangalore UniversityBangalore 560056India

Linear and weakly nonlinear analyses are made for the Rayleigh-Benard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifurcations are presented. The lorenz model is used to study the inverted bifurcation. Positive values of the Soret coefficient favor a pitchfork bifurcation, whereas negative values favor a Hopf bifurcation. Takens-Bogdanov and codimension-two bifurcations are not as much influenced by the Soret coefficient as pitchfork and Hopf bifurcations. The influence of the Soret coefficient on the inverted bifurcation is similar to the influence on the pitchfork bifurcation. The in- fluence of other parameters on the aforementioned bifurcations is also similar as reported earlier in the literature. Using the Newell-Whitehead-Segel equation, the condition for occurrence of Eckhaus and zigzag secondary instabilities is obtained. The domain of ap- pearance of Eckhaus and zigzag instabilities expands due to the presence of the Soret coefficient for positive values. The Soret coefficient with negative values enhances heat transport, while positive values diminish it in comparison with heat transport for the case without the Soret effect. The dual nature of other parameters in influencing heat and mass transport is shown by considering positive and negative values of the Soret coefficient.

关键词： codimension-two Eckhaus inverted lorenz Newell-Whitehead-Segel,Nusselt number Rayleigh-B^nard secondary instability Sherwood number Takens-Bogdanov zigzag

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