Chapter 9.3, Problem 10E

Interpretation Introduction

Interpretation:

To illustrate the “time horizon” after which prediction becomes impossible. To numerically integrate the Lorenz equations for $\text{r = 28}$, $\text{σ = 10}$, $\text{b = }\frac{\text{8}}{\text{3}}$. To start two trajectories from the nearby initial conditions, and to plot $\text{x}\left(\text{t}\right)$ for both of them on the same graph.

Concept Introduction:

• ➢ The Lorenz equations are given as

  $\dot{\text{x}}=\text{σ}\left(\text{y - x}\right)$,

  $\dot{\text{y}}=\text{rx - xz - y}$,

  $\dot{\text{z}}=\text{xy - bz}$

  Here, $\text{σ, r, b > 0}$.