Lorenz系统数值解存疑

Something about the numerical solutions to the Lorenz system

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。

Abstract: 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.