Chapter 10.4, Problem 9E

Interpretation Introduction

Interpretation:

To solve the Lorenz equations numerically for $\text{σ =10, b =}\frac{\text{8}}{\text{2}}\text{,r =148}\text{.5}$; find the stable limit cycle for this condition. Repeating the experiment for $\text{r =147}\text{.5}$. Observe wether the period-doubling occurs or not.

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 the bounded region of the phase space.