作者:  

陈璇:数值计算研究中心,广州

关键词:
Lorenz系统混沌解显式数值Lorenz system; chaotic solutions; numerical method in explicit time scheme

摘要:

Lorenz系统是有E. Lorenz先生于1963年提出的一个典型的混沌系统,该系统在Lorenz先生给出的典型参数(σ = 10, ρ = 28, β = 8/3)下的显式(Runge-Kutta)数值解具有混沌效应,即,初值敏感性。该系统进一步导致大气海洋可预报性问题及资料同化问题,然而这些数值解仍然存在一定的基础性数学问题。本文将这些问题提出,希望得到解答和关注。

Lorenz system is a typical chaotic system by Dr. E. Lorenz (1963), with the typical parameters (σ = 10, ρ = 28, β = 8/3), by using numerical method in explicit time scheme (such as Runge-Kutta method), the numerical solutions to this system are chaotic, which means the numerical solutions are sensitive dependence on initial conditions. On the basis of this system, atmosphere-oceanic predictability and data assimilation were educed, but there are some basic mathematic problems nonsupport the chaotic solutions. In this paper, we will propose these problems, and want these can be solved and attracted attentions.

文章引用:
陈璇. Lorenz系统数值解存疑[J]. 汉斯预印本, 2018, 3(1): 1-8. https://doi.org/10.12677/HANSPrePrints.2018.31001

参考文献

[1] E. N. Lorenz. Deterministic nonperiodic flow. Journal of the Atmospheric Sciences. 20, (1963), 130-141.
[2] Morris W. Hirsch. Smale, Stephen & Devaney, Robert L. Differential equations, dynamical systems, and an introduction to chaos (Third edition). Singapore: Elsevier (Singapore) Pte Ltd, 2015.
[3] Eugenia Kalnay. Atmospheric Modeling, Data Assimilation and Predictability. New York: Cambridge University Press, 2002.
[4] N. Razali & Ahmad R. Rozita. Ahmad R. Solving Lorenz system by using Runge-Kutta method. European Journal of Scientific Research. 2, (2009), 241-251
[5] 香港天文台. 数值天气预报基础课程. 香港天文台: http://www.hko.gov.hk, 2010.
[6] H. G. 舒斯特. 混沌学引论(朱鋐雄, 林圭年, 丁达夫 译). 成都: 四川教育出版社, 2010.
[7] Michael Brin, Garrett Stuck. 动力系统引论(金成桴 译). 北京: 高等教育出版社, 2013.
[8] 黄永念. 非线性动力学引论. 北京: 北京大学出版社, 2010.
[9] 刘秉正, 彭建华. 非线性动力学. 北京: 高等教育出版社, 2004.
[10] 朱华, 姬翠翠. 分形理论及其应用. 北京: 科学出版社, 2011.
[11] A. H. 柯尔莫戈洛夫, C. B. 佛明. 函数论与泛函分析初步(段虞容, 郑洪深, 郭思旭 译). 北京: 高等教育出版社, 2006.
[12] Chen, Xuan. Numerical Counterexamples of Lorenz System in Implicit Time Scheme. Preprints 2018, 2018010277 (doi: 10.20944/preprints201801.0277.v1).