Chapter 9.3, Problem 9E

Interpretation Introduction

Interpretation:

To estimate the largest Liapunov exponent for the Lorenz system, assuming that the parameters have their standard values $\text{r = 28}$, $\text{σ = 10}$, and $\text{b = }\frac{\text{8}}{\text{3}}$, by using the numerical integration of two nearby trajectories.

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, $\text{σ, r, b > 0}$.