Chapter 9.3, Problem 5E

Interpretation Introduction

Interpretation:

To plot $\text{x}\left(\text{t}\right)$, $\text{y}\left(\text{t}\right)$, and $\text{x}$ vs. $\text{z}$ to explore the dynamics of the Lorenz system, for $\text{r = 100}$, assuming $\text{σ = 10}$ and $\text{b = }\frac{\text{8}}{\text{3}}$. To investigate the consequences of choosing different initial conditions and lengths of integration.

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, $\text{σ, r, b > 0}$.