Lorenz Equations 之研究

Abstract

Lorenz Equations 是由三個參數所構成的三維常微分方程式，當參數改變時，方程式解之軌跡將有不同的情形產生，這其中也包括了混沌現象。在此篇論文中，我們藉著Mathematica來描繪方程式解之圖形，以便討論在不同參數值時，Lorenz系統的軌跡及其穩定性。

Lorenz system is a three-parameter family of three-dimensional ordinary differential equations. As we vary the parameters, we change the behavior of the flow determined by the equations. For some values, we see "chaos". To discuss the behavior at different parameters, and the stability of the Lorenz equations, we developed numerical codes to sketch the graphs of the Lorenz equations.