Chapter 9.5, Problem 1E

Interpretation Introduction

Interpretation:

To explore the dynamics of the Lorenz system by using computer for $\text{σ = 10, b = 8/3, r = 166}\text{.3}$ and plot $\text{x(t), y(t) and x vs}\text{. z}$ graphs.

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 the Lorenz equations oscillates irregularly for a wide range of parameters, never exactly repeating but always remaining in a bounded region of the phase space.