Chapter 9.5, Problem 4E

Interpretation Introduction

Numerically integrate the Lorenz equations for $\text{σ = 10, b = 8/3, r = 24}\text{.4 + sinωt}$ and plot the solutions.

Concept Introduction:

Lorenz equations

$\begin{array}{l}\dot{\text{x}}=\sigma (\text{y}-\text{x})\\ \dot{\text{y}}=\text{rx}-\text{y}-\text{xz}\\ \dot{\text{z}}=\text{xy}-\text{bz}\\ \text{Here σ, r, b > 0}\end{array}$

The solution of Lorenz equations oscillates irregularly for a wide range of parameters,

never exactly repeating but always remains in a bounded region of phase space.