论文标题:Lorenz界壳模型系统的非线性动力学分析
Nonlinear Dynamics Analysis on Lorenz Jieke Model System
论文作者 王立媛
论文导师 肖青,论文学位 硕士,论文专业 课程与教学论
论文单位 东北师范大学,点击次数 656,论文页数 42页File Size585k
2005-06-01论文网 http://www.lw23.com/lunwen_943777/ Lorenz 模型; 界壳; 非线性动力学; 代替数据法; 混沌
Lorenz model; Jieke; nonlinear dynamics ; method of surrogate data; chaos
自从 1963 年 E.N.Lorenz 创立了 Lorenz 系统以来,至今人们已经对这个系统进行了大量而深入的研究。到目前为止,Lorenz 系统的动力学行为已经比较清楚,并且 Lorenz 方程可以作为许多混沌现象的精确模型。Mischaikow 和 Mrozek两人从理论上证明了 Lorenz 系统存在混沌行为。但是从 Lorenz 系统所描述的气象角度来考虑,Lorenz 方程中的 Prandtl 数σ 取 10 时系统才能表现出湍流现象(即混沌行为),但σ 取 10 是不合理的,系统不能描述大气的真实情况,因为对于大气,σ 约为 0.7。大气科学中讲,风速垂直切变对大气湍流也有贡献。将这一因素考虑到系统中来,并从界壳角度给予了解释。“界壳”这一概念是中国气象研究院研究员曹鸿兴提出,界壳理论已在熵平衡、动力学、非线性、几何模型等多个方面得到了颇为成效的成果,但还不是很成熟。本文从界壳的角度来考虑 Lorenz 系统,将方程中加进风速垂直切变后得到了一个新的模型。这时的模型我们就称为 Lorenz 界壳模型系统。为了弄清楚 Lorenz 界壳模型系统的动力学特性,对系统进行了一系列的非线性动力学分析,如功率谱、重现图形、相空间重构、庞卡莱截面法,这些特征量是从定性的角度来分析,而关联维、最大李氏指数是从定量的角度进行分析。此外,我们还采用代替数据法进行了关联维、最大李氏指数等特征量的分析。这些分析结果表明 Lorenz 界壳模型系统仍然存在混沌行为。
Since the E.N.Lorenz established the system of Lorenz in 1963, the people havealready done a lot of work on this system. The dynamics behavior of the system ofLorenz already more and clearly, and the square distance of Lorenz can be accuratemodel of many phenomenon mentally dense sport. Mischaikow and Mrozek provedthe Lorenz system existence mentally dense behavior from the theories. Butconsidered the weather described by the system of Lorenz, The Lorenz Prandtlnumber within square distance takes the system to then can express a swift flowphenomenon( namely chaos behavior)10, but take 10 is not reasonable, the systemcan"t describe the true circumstance of the atmosphere, because of for atmosphere,Prandtl number about 0.7. In the Atmospheric Sciences, the wind velocityperpendicularity slices to become to also have contribution to the atmosphere swiftflow. This thesis considered the factor and give the from Jieke. " Jieke" is first put forward by Hong Xing Cao who is the researcher of Chineseweather institute for research. The Jieke theories already in the approximate balance,dynamics and not line, several model etc. This thesis considered the system of Lorenzfrom the angle of the Jieke. adding in the square distance into the wind velocityperpendicularity to get a new model after slice become. We called the model to beLorenz Jieke model system. For clearing up the dynamics characteristic of the Lorenz Jieke model system, Ido a series un-line dynamics analysis on the system, such as phase spectrum,recurrence plot, reconstructing the state space, and pangkalai space cuts to face areassayed in qualitative. The correlation dimension and largest Lyapunov exponents areassayed in quantitative. In addition, we adopt to the method of surrogate data to assaythe correlation dimension and largest Lyapunov exponents. All analysis resultsexpress that the Lorenz Jieke model system still exists the mentally dense behavior.
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