不依赖数据库的最优动力系统建模理论及其应用  

A NEW DATABASE-FREE METHOD OF CONSTRUCTING OPTIMAL LOW-DIMENSIONAL DYNAMICAL SYSTEMS AND ITS APPLICATION

作　　者：吴锤结[1] 赵红亮[2] 

机构地区：[1]中国科学院力学研究所非线性力学国家重点实验室,北京100080 [2]解放军理工大学理学院流体力学研究中心,南京211101

出　　处：《力学学报》2001年第3期289-300,共12页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(19472077);中国科学院力学所非线性力学国家重点实验室;北京大学湍流研究国家重点实验室资助 项目.

摘　　要：在Ｗｕ提出的流动数据库分析及建立低维动力系统的优化理论基础上，进一步提出不依赖于数据库、直接由偏微分方程构造最优低维动力系统的方法．以二维热对流问题为例求得五维最优低维动力系统，研究其动力学特性，并与Ｌｏｒｅｎｚ模型进行比较．结果表明：该方法无需依赖数据库即可提取真实反映复杂流动动力学特征的最优基，建立在最优基之上的动力系统更充分地描述了问题的复杂动力学行为，并揭示了一些新的动力学特征．Based on the theory of constructing optimal Low-Dimensional Dynamical Systems (LDDS), either based on known databases or directly from partial differential equations, (Wu CJ, Discrete and Continuous Dynamical Systems. 1996, 2(4): 559～583), a new method of building optimal LDDS models directly from partial differential equations is proposed in this paper. A 5 dimensional optimal LDDS of Lorenz system is obtained with the new method, and its dynamical characters are studied. Results show that the new method does not depend on flow database and has the ability to capture the typical characters of complicated fluid problems. There are some new complicated dynamical properties in the 5 dimensional optimal LDDS, which are not exist in the classical Lorenz model.

关 键 词：偏微分方程 动力系统 LORENZ系统 功率谱 LYAPUNOV指数 力学 数据库 建模 

分 类 号：O351.2[理学—流体力学]